WAM

WAM (Weighted Arithmetic Mean) is a aggregationoperator multi-criteria decision-making (MCDM) method introduced by Yager, R. R. in 1988. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems, Man, and Cybernetics


Washability

Washability Analysis for Coal and Minerals

Coal Washability
Density Separation Analysis
Float-Sink Analysis

Washability analysis is a laboratory method that determines the feasibility and efficiency of density-based separation for coal or mineral beneficiation. By fractionating ore or coal into density bins using sink-float tests and assaying each fraction, engineers can optimize design of separation plants (dense-medium cyclones, jigs, spirals) and predict clean product quality. Washability curves are essential tools for pre-feasibility and detailed design studies.

Separation analysis by density fractionation

McCullough, R. B. (1963). The theoretical basis and practical application of coal washability studies. Transactions of the Society of Mining Engineers, 226, 13-26.

Clarkson, T. E., & Trevits, M. A. (2000). Coal preparation and resource utilization in United States. Bureau of Mines Information Circular IC 9413.


WASPAS

WASPAS (Weighted Aggregated Sum Product Assessment) is a ranking multi-criteria decision-making (MCDM) method introduced by Zavadskas, E. K., Turskis, Z., Antucheviciene, J., Zakarevicius, A. in 2012. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Zavadskas, E. K., Turskis, Z., Antucheviciene, J., Zakarevicius, A. (2012). Optimization of weighted aggregated sum product assessment. Elektronika ir Elektrotechnika

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


Wasserstein GAN

Wasserstein Generative Adversarial Network

Martín Arjovsky, Soumith Chintala & Léon Bottou

Wasserstein GAN (WGAN) is a generative adversarial network variant introduced by Arjovsky, Chintala, and Bottou in 2017 that replaces the Jensen-Shannon divergence used in the original GAN with the Wasserstein-1 (Earth Mover) distance. This substitution provides a theoretically grounded training objective that yields more stable optimization and a loss value that correlates meaningfully with generated sample quality, addressing the notorious mode collapse and vanishing gradient problems of standard GANs.

Weight clipping (critic weights clipped to compact space)

Arjovsky, M., Chintala, S., & Bottou, L. (2017). Wasserstein generative adversarial networks. International Conference on Machine Learning (ICML), 214–223.


Wastewater Treatment Design

Multi-Stage Wastewater Treatment Plant Design and Optimization

WWTP design
sewage treatment
water reclamation
municipal treatment

Wastewater treatment design is the comprehensive planning and engineering of municipal and industrial treatment plants to remove contaminants (organic matter, nutrients, pathogens, trace organics) from domestic and industrial wastewater. Modern treatment plants integrate preliminary screening, primary settlement, secondary biological treatment (activated sludge, trickling filters, lagoons), advanced treatment (membrane filtration, oxidation, absorption), sludge processing, and biosolids management. The design balances regulatory compliance, treatment performance, energy consumption, land use, and capital and operational cost.

integrated design and optimization pipeline

Metcalf & Eddy, Inc. (2013). Wastewater Engineering: Treatment and Resource Recovery (5th ed.). McGraw-Hill.

Tchobanoglous, G., Stensel, H. D., Tsuchihashi, R., Burton, F. L., Abu-Orf, M., Bowden, G., & Pfrang, W. (2014). Wastewater Engineering: Treatment and Resource Recovery (5th ed.). McGraw-Hill.

US Environmental Protection Agency. (2004). Wastewater Technology Fact Sheets: Sequencing Batch Reactors. EPA 832-F-04-018.


Waterlow Scale
Pressure Ulcer Risk Assessment
Waterlow Score

The Waterlow Pressure Injury Risk Assessment Scale, developed by Judy Waterlow in 1985, is a widely used clinical tool in nursing for identifying patients at risk of developing pressure injuries (formerly called pressure ulcers or bedsores). The scale evaluates multiple risk factors including age, mobility, skin condition, weight/body mass index, appetite, and incontinence status, generating a numerical risk score that guides preventive care intensity. It is standard in hospital, long-term care, and community nursing settings across the United Kingdom, Europe, and internationally.

Waterlow, J. (1985). A risk assessment tool for pressure sores. Nursing Times, 81(48), 49-55.

Waterlow, J. (2005). Pressure ulcers: Avoidance and treatment. Nursing Times, 101(12), 58-61.


Watershed Segmentation

Watershed Algorithm for Image Segmentation

Watershed transform
Water shedding segmentation

Watershed segmentation is a morphological image processing technique that automatically segments an image into distinct regions by treating image intensity as a topographic landscape where each object corresponds to a valley. Introduced by Beucher and Lantuéjoul in 1979 and refined by Meyer, the watershed algorithm is particularly effective for separating touching or overlapping objects.

Meyer, F. (1994). Topographic distance and watershed lines. Signal Processing, 38(1), 113–125.

Beucher, S., & Lantuéjoul, C. (1979). Use of watersheds in contour detection. International Workshop on Image Processing, Real-Time Edge and Motion Detection/Estimation, 2.1–2.12.

image-morphology contour-analysis canny-edge-detection blob-detection histogram-equalization


Wavelet Coherence

WTC
Wavelet coherency
Continuous wavelet coherence

Wavelet coherence (WTC) is a normalized measure of correlation between two time series in the time-frequency domain, eliminating the amplitude-dependence of the raw cross-wavelet transform. Introduced by Torrence and Webster (1999) and formalized by Grinsted, Moore, and Jevrejeva (2004), WTC quantifies how tightly two signals are coupled at each time-frequency point, independent of their individual power levels. It is the wavelet analog of classical spectral coherence, revealing time-localized relationships across all frequencies.

Torrence, C., & Webster, P. J. (1999). Interdecadal changes in the ENSO–monsoon system. Journal of Climate, 12(8), 2679–2690.

Grinsted, A., Moore, J. C., & Jevrejeva, S. (2004). Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics, 11(5–6), 561–566.

Maraun, D., Kurths, J., & Holschneider, M. (2007). Nonstationary Gaussian processes in wavelet domain: synthesis, estimation, and significance testing. Physical Review E, 75(1), 016707.

cross-wavelet-transform continuous-wavelet-transform cross-correlation spectral-coherence


Wavelet Financial Analysis

Wavelet Analysis of Financial Time Series

wavelet coherence
continuous wavelet transform
time-frequency analysis
Dalgacık (Wavelet) Finansal Analiz

Gençay, Selçuk & Whitcher; Aguiar-Conraria & Soares

Wavelet financial analysis decomposes a financial time series into different frequency bands (time scales) so short- and long-term relationships can be studied at the same time. Drawing on the treatments of Gençay, Selçuk and Whitcher (2001) and Aguiar-Conraria and Soares (2014), wavelet coherence then visualises how the relationship between two series shifts across both time and frequency.

Wavelet transform (Morlet); wavelet coherence

Gençay, R., Selçuk, F. & Whitcher, B. (2001). An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. Academic Press.

Aguiar-Conraria, L. & Soares, M.J. (2014). The Continuous Wavelet Transform: Moving Beyond Uni- and Bivariate Analysis. Journal of Economic Surveys, 28(2), 344-375.

regime-switching-finance garch-volatility arima-forecasting spectral-analysis var-time-series


Wavelet Neural Network

WNN
Wavelet-based neural network
Wavelet networks

Wavelet-based activation function network

A wavelet neural network (WNN) is a function approximation architecture that uses wavelet functions as activation functions in place of traditional sigmoid or ReLU functions. Introduced by Zhang and Benveniste (1992), WNNs combine the multiscale decomposition properties of wavelets with the learning capabilities of neural networks. The result is a flexible nonparametric model that can capture localized features and multi-resolution patterns efficiently, with fewer parameters and better interpretability than standard deep networks.

Zhang, Q., & Benveniste, A. (1992). Wavelet networks. IEEE Transactions on Neural Networks, 3(6), 889–898.

Pati, Y. C., & Krishnaprasad, P. S. (1992). Nonlinear dynamics and signal processing in the cochlea. ICASSP, pp. V373–V376.

Misiti, M., Misiti, Y., Oppenheim, G., & Poggi, J. M. (1997). Wavelet Toolbox. The Mathworks.

radial-basis-function-network multilayer-perceptron convolutional-neural-network recurrent-neural-network


Wayfinding Analysis

Wayfinding Analysis and Navigation Assessment

way-finding assessment
navigation design analysis
signage and circulation analysis

Wayfinding Analysis is a method for assessing how easily people can navigate and orient themselves in buildings and urban environments. Rooted in Kevin Lynch's concept of legibility and developed further by Romedi Passini, it combines cognitive psychology, design principles, and empirical testing to diagnose navigation difficulties and design intuitive navigation systems.

navigation and spatial orientation assessment method

Lynch, K. (1960). The Image of the City. MIT Press, Cambridge, MA.

Passini, R. (1992). Wayfinding in Architecture. Van Nostrand Reinhold, New York.

Arthur, P., Passini, R. (1992). Wayfinding: People, Signs, and Architecture. McGraw-Hill Professional.


Weak Gravitational Lensing

Weak Gravitational Lensing for Dark Matter and Cosmology

Weak Lensing
Cosmic Shear
Lensing Distortion

Weak gravitational lensing occurs when light from distant sources bends slightly as it travels through the universe, passing through the gravitational fields of matter concentrations. Proposed theoretically by Nick Kaiser in 1992, this subtle effect has become one of the most powerful cosmological probes, directly revealing the distribution of all matter (dark and luminous) across cosmic distances.

Kaiser, N. (1992). Weak gravitational lensing of distant galaxies. Astrophysical Journal, 388, 272-286.

Van Waerbeke, L., et al. (2000). Detection of weak gravitational lensing by large-scale structure. Astronomy & Astrophysics, 358, 30-44.

Hildebrandt, H., et al. (2020). KiDS+VIKING-450 and S-PLUS: Cosmic shear measurements with 1,346 square degrees. Astronomy & Astrophysics, 633, A69.


Weakly Supervised BERT-based Text Classification

WS-BERT
BERT with weak supervision
label-efficient BERT classification
noisy-label BERT fine-tuning

Multiple (Ratner et al. for weak supervision framework; Meng et al. for BERT integration)

Weakly supervised BERT-based classification adapts BERT to text classification tasks when only noisy, heuristic, or programmatically generated labels are available instead of clean human annotations. It combines weak supervision frameworks — such as labeling functions and data programming — with BERT's pre-trained language representations to achieve robust classification without expensive hand-labeling.

Weakly supervised fine-tuning of pre-trained language model

Text (labeled, noisy-labeled, or label-rule-generated)

Meng, Y., Zhang, Y., Huang, J., Xiong, C., Ji, H., Zhang, C., & Han, J. (2020). Text Classification Using Label Names Only: A Language Model Self-Training Approach. Proceedings of EMNLP 2020, 9006–9017.

Ratner, A., Bach, S. H., Ehrenberg, H., Fries, J., Wu, S., & Re, C. (2017). Snorkel: Rapid Training Data Creation with Weak Supervision. Proceedings of the VLDB Endowment, 11(3), 269–282.


Weakly supervised convolutional neural network

Weakly Supervised Convolutional Neural Network

WS-CNN
weakly supervised CNN
CNN with weak labels
CNN with noisy labels

A weakly supervised CNN is a convolutional neural network trained with incomplete, coarse, or noisy annotations instead of full pixel-level or bounding-box labels. Typical weak labels include image-level class tags, partial annotations, or crowd-sourced noisy labels. The model learns to classify and often to roughly localize objects using these cheaper, lower-quality supervision signals.

Images with coarse or image-level labels

Zhou, B., Khosla, A., Lapedriza, A., Oliva, A., & Torralba, A. (2016). Learning deep features for discriminative localization. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2921–2929.

Oquab, M., Bottou, L., Laptev, I., & Sivic, J. (2015). Is object localization for free? — Weakly-supervised learning with convolutional neural networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 685–694.


Weakly Supervised Diffusion Model

Weakly Supervised Diffusion Model (Denoising Diffusion with Imperfect Supervision)

WS-Diffusion
weakly supervised DDPM
label-efficient diffusion model
noisy-label diffusion training

Ho et al. (DDPM foundation); weak supervision integration by multiple groups, 2022–2024

A weakly supervised diffusion model trains or conditions a denoising diffusion probabilistic model using coarse, noisy, or incomplete supervision signals — such as image-level class labels, bounding boxes, or crowd-sourced annotations — instead of pixel-precise ground truth. This allows high-quality generative and discriminative outputs in annotation-scarce settings where full labeling is infeasible or prohibitively expensive.

Generative model with imperfect supervision

Images, image-level labels, noisy annotations, partial masks

Ho, J., Jain, A., & Abbeel, P. (2020). Denoising Diffusion Probabilistic Models. Advances in Neural Information Processing Systems (NeurIPS), 33, 6840–6851.

Zhou, K., et al. (2023). Weakly-supervised Semantic Segmentation with Diffusion Models. arXiv preprint arXiv:2309.11803.

diffusion-model semi-supervised-diffusion-model weakly-supervised-semantic-segmentation self-supervised-diffusion-model generative-adversarial-network variational-autoencoder


Weakly supervised GAN

Weakly Supervised Generative Adversarial Network

weakly supervised generative adversarial network

Odena et al.; building on Goodfellow et al. (2014)

A Weakly Supervised GAN is a generative adversarial network trained with partially labeled, noisily labeled, or coarse-annotation data instead of fully annotated ground truth. It extends the standard GAN framework so that limited supervision guides conditional generation or discriminative learning, enabling high-quality data synthesis and classification in label-scarce settings.

Images, tabular data, or sequences with partial or noisy labels

Odena, A., Olah, C., & Shlens, J. (2017). Conditional Image Synthesis with Auxiliary Classifier GANs. Proceedings of the 34th International Conference on Machine Learning (ICML), PMLR 70, 2642–2651.

Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., & Bengio, Y. (2014). Generative Adversarial Nets. Advances in Neural Information Processing Systems (NeurIPS), 27.

generative-adversarial-network semi-supervised-gan conditional-gan weakly-supervised-image-classification variational-autoencoder diffusion-model


Weakly supervised graph neural network

graph neural network with weak supervision

Derived from GNN literature (Scarselli et al. 2009; Kipf & Welling 2017) combined with weak supervision paradigm

A Weakly Supervised Graph Neural Network (WS-GNN) is a graph deep-learning approach that learns from graph-structured data — nodes, edges, and their attributes — when only noisy, partial, or indirectly obtained labels are available. By coupling GNN message passing with noise-robust training strategies, it extends graph learning to real-world settings where clean, fully annotated graphs are scarce or expensive to obtain.

Graph-based deep learning with imperfect supervision

Graph-structured data (nodes, edges, attributes) with noisy, incomplete, or indirect labels

Kipf, T. N., & Welling, M. (2017). Semi-supervised classification with graph convolutional networks. In Proceedings of the 5th International Conference on Learning Representations (ICLR 2017).

Zhou, J., Cui, G., Hu, S., Zhang, Z., Yang, C., Liu, Z., Wang, L., Li, C., & Sun, M. (2020). Graph neural networks: A review of methods and applications. AI Open, 1, 57–81.


Weakly Supervised GRU

Weakly Supervised Gated Recurrent Unit Network

WS-GRU
GRU with weak supervision
weakly labeled GRU
noisy-label GRU

Chung et al. (GRU); Ratner et al. (weak supervision framework)

Weakly Supervised GRU trains a Gated Recurrent Unit network on sequences labeled by imperfect, heuristic, or programmatic sources rather than costly hand-annotated ground truth. It combines the GRU's efficiency at capturing temporal dependencies with weak-supervision techniques that aggregate noisy labels, enabling practical sequence modeling when large fully labeled datasets are unavailable.

Sequential / time-series / text with noisy or heuristic labels

Ratner, A. J., De Sa, C. M., Wu, S., Selsam, D., & Re, C. (2016). Data Programming: Creating Large Training Sets, Quickly. Advances in Neural Information Processing Systems (NeurIPS), 29.

Chung, J., Gulcehre, C., Cho, K., & Bengio, Y. (2014). Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling. NIPS 2014 Workshop on Deep Learning.

gated-recurrent-unit weakly-supervised-lstm weakly-supervised-transformer semi-supervised-gru recurrent-neural-network long-short-term-memory


Weakly Supervised Image Classification

Weakly Supervised Image Classification (WSL-IC)

WSL image classification
image-level supervised classification
noisy-label image classification
weakly labeled visual recognition

Multiple contributors; class activation map approach: Zhou et al.

Weakly supervised image classification trains convolutional or transformer-based networks using only coarse, incomplete, or noisy supervision — such as image-level category labels, hashtags, or web-scraped tags — without requiring precise bounding boxes or pixel annotations. This dramatically reduces labeling cost while still enabling high-accuracy visual recognition at scale.

Weakly supervised deep learning paradigm

Images with image-level labels, noisy labels, or web-crawled annotations

Zhou, B., Khosla, A., Lapedriza, A., Oliva, A., & Torralba, A. (2016). Learning Deep Features for Discriminative Localization. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2921–2929.

Mahajan, D., Girshick, R., Ramanathan, V., He, K., Paluri, M., Li, Y., Bharambe, A., & van der Maaten, L. (2018). Exploring the Limits of Weakly Supervised Pretraining. Proceedings of the European Conference on Computer Vision (ECCV), 181–196.


Weakly Supervised Instance Segmentation

Weakly Supervised Instance Segmentation (Deep Learning with Incomplete Annotations)

WSIS
weakly-supervised mask prediction
weak-label instance segmentation
box-supervised instance segmentation

Multiple contributors (e.g., Hsu et al., Khoreva et al.)

Weakly supervised instance segmentation trains deep networks to delineate individual object instances at pixel level using only cheap, incomplete annotations — such as bounding boxes, image-level labels, or point clicks — rather than costly full pixel-wise masks. It dramatically reduces annotation effort while still producing instance-level masks for each object in an image.

Weakly supervised deep learning for pixel-wise instance delineation

Image data with weak annotations (bounding boxes, image-level labels, or point clicks)

Hsu, C.-C., Hsu, K.-J., Tsai, C.-C., Lin, Y.-Y., & Chuang, Y.-Y. (2019). Weakly supervised instance segmentation using the bounding box tightness prior. Advances in Neural Information Processing Systems (NeurIPS), 32.

Zhou, B., Khosla, A., Lapedriza, A., Oliva, A., & Torralba, A. (2016). Learning deep features for discriminative localization. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2921–2929.

instance-segmentation semantic-segmentation weakly-supervised-semantic-segmentation object-detection semi-supervised-instance-segmentation self-supervised-instance-segmentation


Weakly supervised LDA topic model

Weakly Supervised Latent Dirichlet Allocation Topic Model

WS-LDA
Guided LDA
Seeded LDA
Constrained LDA

Weakly Supervised LDA is an extension of Latent Dirichlet Allocation that incorporates lightweight human guidance — typically keyword seeds or must-link/cannot-link constraints — into the Dirichlet priors, steering learned topics toward domain-meaningful themes without requiring fully labeled documents. It sits between fully unsupervised LDA and supervised classification, making it well-suited to situations where labeling thousands of documents is impractical.

Probabilistic generative model with weak supervision

Jagarlamudi, J., Daume III, H., & Udupa, R. (2012). Incorporating Lexical Priors into Topic Models. Proceedings of the 13th Conference of the European Chapter of the Association for Computational Linguistics (EACL 2012), pp. 204–213.

Andrzejewski, D., Zhu, X., & Craven, M. (2009). Incorporating Domain Knowledge into Topic Modeling via Dirichlet Forest Priors. Proceedings of the 26th International Conference on Machine Learning (ICML 2009), pp. 25–32.


Weakly supervised LSTM

Weakly Supervised Long Short-Term Memory Network

WS-LSTM
noisy-label LSTM
distant-supervision LSTM
data-programming LSTM

Ratner et al. (data programming framework); Hochreiter & Schmidhuber (LSTM backbone)

Weakly supervised LSTM trains a Long Short-Term Memory network on sequence data where clean, manually annotated labels are scarce or absent. Instead, multiple imperfect label sources — heuristic rules, distant supervision, crowdsourcing, or programmatic labeling functions — are combined to produce probabilistic training labels, which are then used to supervise the LSTM. This allows scalable training on large unlabeled corpora without exhaustive human annotation.

Sequential / text data with noisy or heuristic labels

Ratner, A., De Sa, C., Wu, S., Selsam, D., & Re, C. (2016). Data Programming: Creating Large Training Sets, Quickly. Advances in Neural Information Processing Systems (NeurIPS), 29.

Zhou, Z.-H. (2018). A brief introduction to weakly supervised learning. National Science Review, 5(1), 44–53.


Weakly supervised multilayer perceptron

WS-MLP
weakly supervised feedforward network
noisy-label MLP
weak-label multilayer perceptron

Multiple contributors; paradigm formalized by Zhou (2018) and Ratner et al. (2016)

A Weakly Supervised Multilayer Perceptron trains a standard feedforward neural network when only imperfect supervision is available — labels may be noisy, incomplete, crowd-sourced, rule-generated, or derived from distant supervision — enabling learning at scale without the cost of full expert annotation.

Feedforward neural network trained under weak supervision

Tabular, text, or image features with noisy, incomplete, or programmatically generated labels

Ratner, A. J., De Sa, C. M., Wu, S., Selsam, D., & Re, C. (2016). Data programming: Creating large training sets, quickly. Advances in Neural Information Processing Systems (NeurIPS), 29.


Weakly Supervised Object Detection

WSOD
weakly-supervised detection
image-level supervised detection
multiple instance detection

Bilen, H. & Vedaldi, A. (WSDDN); Multiple Instance Learning origins: Dietterich et al. (1997)

Weakly Supervised Object Detection (WSOD) trains object detectors using only image-level labels — indicating which object classes appear in an image — without requiring costly bounding-box annotations. Multiple Instance Learning (MIL) formulations allow the model to discover the likely location of each object class from classification signals alone, dramatically reducing annotation cost.

Images with image-level classification labels (no bounding boxes)

Bilen, H., & Vedaldi, A. (2016). Weakly supervised deep detection networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2846–2854.

Tang, P., Wang, X., Bai, X., & Liu, W. (2017). Multiple instance detection network with online instance classifier refinement. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2843–2851.

object-detection image-classification semi-supervised-object-detection instance-segmentation convolutional-neural-network vision-transformer


Weakly supervised question answering

WS-QA
distantly supervised QA
noisy-label question answering
indirect supervision QA

Multiple authors (Clark, Gardner, Min et al.)

Weakly supervised question answering (WS-QA) trains neural reading-comprehension models using indirect or automatically derived answer labels rather than expensive human-annotated span annotations. By exploiting distant supervision, heuristic labeling, or answer-presence signals, WS-QA makes QA feasible in domains and languages where full annotation is impractical.

Text passages, questions, and weak/distant answer labels

Clark, C., & Gardner, M. (2018). Simple and Effective Multi-Paragraph Reading Comprehension. In Proceedings of ACL 2018, pp. 845–855. Association for Computational Linguistics.

Min, S., Chen, D., Hajishirzi, H., & Zettlemoyer, L. (2019). A Discrete Hard EM Approach for Weakly Supervised Question Answering. In Proceedings of EMNLP-IJCNLP 2019, pp. 2083–2093. Association for Computational Linguistics.


Weakly supervised recurrent neural network

Weakly Supervised Recurrent Neural Network

WS-RNN
distantly supervised RNN
noise-tolerant RNN
weakly supervised sequence model

Broadly attributed to the weak supervision / distant supervision research community (Mintz et al., 2009; Ratner et al., 2016)

A weakly supervised RNN trains a recurrent neural network on sequences whose labels come from imperfect sources — heuristic rules, distant supervision, crowdsourcing, or generative label models — rather than expensive expert annotation. This lets researchers exploit large unlabeled corpora for sequential tasks such as text classification, named entity recognition, or time-series prediction when fully annotated data is scarce or costly.

Supervised learning under noisy or incomplete labels

Sequential data (text, time series, speech)


Weakly Supervised Reinforcement Learning

WSRL
weak-reward RL
imperfect-reward reinforcement learning
reward-impoverished RL

Multiple contributors; reward-learning framing: Christiano et al. (2017)

Weakly supervised reinforcement learning (WSRL) trains agents in environments where the reward signal is imperfect, sparse, delayed, or only partially informative — unlike dense fully-supervised RL. The agent must learn effective policies despite incomplete feedback, using auxiliary signals, reward modeling, or preference learning to compensate for the weak supervision.

Reinforcement learning with imperfect or partial reward supervision

State-action trajectories with weak, noisy, delayed, or sparse reward signals

Sutton, R. S. & Barto, A. G. (2018). Reinforcement Learning: An Introduction (2nd ed.). MIT Press.

Christiano, P., Leike, J., Brown, T. B., Martic, M., Legg, S. & Amodei, D. (2017). Deep reinforcement learning from human preferences. Advances in Neural Information Processing Systems (NeurIPS), 30.

reinforcement-learning semi-supervised-reinforcement-learning self-supervised-reinforcement-learning reward-shaping inverse-reinforcement-learning imitation-learning


Weakly Supervised RoBERTa-based Classification

Weakly Supervised Text Classification with RoBERTa

weakly supervised transformer classification

Liu et al. (RoBERTa, 2019); weak supervision paradigm: Ratner et al. (2016–2020)

Weakly supervised RoBERTa-based classification combines the RoBERTa pretrained transformer with weak supervision — programmatic or heuristic labeling sources — to train powerful text classifiers without requiring a fully hand-labeled dataset. Labeling functions, distant supervision, or crowd-sourced signals generate noisy labels that are aggregated and used to fine-tune RoBERTa for downstream classification tasks.

Pretrained transformer classifier with weak supervision

Text (partially labeled or programmatically labeled corpora)

Liu, Y., Ott, M., Goyal, N., Du, J., Joshi, M., Chen, D., Levy, O., Lewis, M., Zettlemoyer, L., & Stoyanov, V. (2019). RoBERTa: A Robustly Optimized BERT Pretraining Approach. arXiv:1907.11692.

Zhang, J., Yu, Y., Li, Y., Wang, Y., Yang, Y., Yang, M., & Ratner, A. (2021). WRENCH: A Comprehensive Benchmark for Weak Supervision. NeurIPS 2021 Datasets and Benchmarks Track.


Weakly Supervised Semantic Segmentation

WSSS
weak-label segmentation
image-level supervised segmentation
weakly-labeled pixel classification

Multiple contributors; Class Activation Mapping (Zhou et al., 2016) is foundational

Weakly Supervised Semantic Segmentation (WSSS) trains pixel-level scene parsers using only cheap, coarse annotations — typically image-level class tags — instead of costly dense pixel masks. By generating proxy pseudo-labels from a classification network (via Class Activation Maps or similar localisation cues) and iteratively refining them, WSSS brings full-supervision accuracy within reach at a fraction of the annotation cost.

Pixel-level classification with image-level or coarse supervision

Images with weak labels (image-level tags, bounding boxes, or scribbles)

Zhou, B., Khosla, A., Lapedriza, A., Oliva, A., & Torralba, A. (2016). Learning Deep Features for Discriminative Localization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2921–2929.

Ahn, J., & Kwak, S. (2018). Learning Pixel-Wise Semantic Affinity with Image-Level Supervision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4109–4118.

semantic-segmentation class-activation-mapping semi-supervised-learning self-supervised-learning object-detection convolutional-neural-network


Weakly supervised sentence embeddings

noisy-label sentence representation learning

weakly supervised sentence representation

Ratner et al. (weak supervision framework); Reimers & Gurevych (sentence embeddings)

Weakly supervised sentence embeddings train dense sentence representations using noisy, heuristic, or programmatically generated labels instead of costly human annotation. Labeling functions — rules, distant supervision signals, or lightweight classifiers — supply approximate supervision that a label model aggregates into probabilistic labels, which then guide the sentence encoder to produce task-useful representations at scale.

Representation learning under weak supervision

Text (sentences, paragraphs); noisy or heuristically labeled corpora

Reimers, N., & Gurevych, I. (2019). Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing (EMNLP).


Weakly supervised text summarization

weak supervision summarization
distantly supervised summarization
noisy-label summarization
pseudo-label summarization

Multiple independent research groups (NLP community, 2010s–2020s)

Weakly supervised text summarization trains abstractive or extractive summarization models without manually annotated reference summaries. Instead of costly human labels, it exploits weak signals — heuristic rules, distant supervision, noisy automatic labels, or self-supervised objectives — to guide sequence-to-sequence or transformer models toward producing coherent, concise summaries of input documents.

Semi-supervised / weakly supervised NLP training paradigm

Unlabeled or noisily labeled text corpora

Amplayo, R. K., & Lapata, M. (2020). Unsupervised Opinion Summarization with Noisy Autoencoder. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, 1934–1945.

Huang, L., Wu, L., & Wang, L. (2020). Knowledge Graph-Augmented Abstractive Summarization with Semantic-Driven Cloze Reward. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, 5094–5107.

extractive-text-summarization abstractive-text-summarization seq2seq-model transformer-model self-supervised-learning distant-supervision


Weakly Supervised Topic Modeling

Weakly Supervised Topic Modeling (Seed-Guided / Constrained Topic Models)

guided topic modeling
seed-guided topic model
constrained topic modeling
seeded LDA

Jagarlamudi, Daume & Udupa; Gallagher et al. (CorEx)

Weakly supervised topic modeling incorporates lightweight domain knowledge — typically seed words or soft constraints — into a probabilistic topic model to steer discovered topics toward researcher-meaningful themes. It sits between fully unsupervised LDA and supervised classifiers, requiring far less annotation than the latter while producing more interpretable and domain-aligned topics than the former.

Weakly supervised probabilistic topic model

Jagarlamudi, J., Daume III, H., & Udupa, R. (2012). Incorporating Lexical Priors into Topic Models. Proceedings of EACL 2012, 204–213.

Gallagher, R. J., Reing, K., Kale, D., & Ver Steeg, G. (2017). Anchored Correlation Explanation: Topic Modeling with Minimal Domain Knowledge. Transactions of the Association for Computational Linguistics, 5, 529–542.


Weakly supervised transformer

WST
weakly supervised attention model
noisy-label transformer
weak supervision with transformers

Multiple contributors (weak supervision paradigm: Zhou 2018; transformer backbone: Vaswani et al. 2017)

Weakly Supervised Transformer combines the representational power of Transformer architectures with weak supervision strategies that exploit noisy, incomplete, or programmatically generated labels — making it possible to train high-quality NLP and vision models when fully annotated datasets are scarce or prohibitively expensive to produce.

Text, image, or multimodal data with noisy or incomplete labels

Ratner, A., Bach, S. H., Ehrenberg, H., Fries, J., Wu, S., & Re, C. (2017). Snorkel: Rapid training data creation with weak supervision. Proceedings of the VLDB Endowment, 11(3), 269–282.

Zhou, Z.-H. (2018). A brief introduction to weakly supervised learning. National Science Review, 5(1), 44–53.


WS-VAE
weakly-supervised VAE
semi-supervised VAE with weak labels
label-guided variational autoencoder

Kingma, D. P. et al. (building on VAE and semi-supervised deep generative models)

A Weakly Supervised Variational Autoencoder (WS-VAE) extends the standard VAE generative framework by incorporating partial, noisy, or coarse supervision signals — such as crowd-sourced labels, heuristic rules, or programmatic annotations — to guide latent space learning without requiring fully annotated data. It is widely applied in computer vision, NLP, and biomedical domains where complete ground-truth labels are expensive or unavailable.

Images, text, or structured data with partial or noisy labels

Kingma, D. P. & Welling, M. (2014). Auto-Encoding Variational Bayes. In Proceedings of the International Conference on Learning Representations (ICLR 2014).

Kingma, D. P., Mohamed, S., Rezende, D. J. & Welling, M. (2014). Semi-supervised learning with deep generative models. In Advances in Neural Information Processing Systems (NeurIPS 2014), 27.

variational-autoencoder semi-supervised-learning beta-vae conditional-vae disentangled-representation-learning generative-adversarial-network


Weakly supervised vision transformer

weak supervision with vision transformer

Dosovitskiy et al. (ViT); weak supervision paradigm from Zhou and others

Weakly Supervised Vision Transformer (WS-ViT) trains a Vision Transformer on image data that lacks precise pixel-level annotations, instead using cheaper, noisier supervision such as image-level class tags, bounding boxes, or web-scraped text. The global self-attention mechanism of the transformer makes it especially capable of localising objects and learning discriminative features from these incomplete labels.

Self-attention image model with weakly supervised training

Image patches with coarse, noisy, or partial labels

Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., & Houlsby, N. (2021). An image is worth 16x16 words: Transformers for image recognition at scale. In International Conference on Learning Representations (ICLR).

Zhou, Z.-H. (2022). A brief introduction to weakly supervised learning. National Science Review, 5(1), 44–53.

vision-transformer semi-supervised-learning self-supervised-learning multiple-instance-learning convolutional-neural-network knowledge-distillation


Weakly supervised Word2Vec

Weakly Supervised Word2Vec (Word Embeddings with Weak Supervision)

WS-Word2Vec
weakly-supervised word embeddings
weak-label Word2Vec
semi-noisy Word2Vec

Mikolov et al. (Word2Vec); weak supervision framework: Ratner et al.

Weakly Supervised Word2Vec trains Word2Vec-style embeddings using automatically generated, noisy, or heuristic labels rather than costly manual annotation. By leveraging labeling functions, distant supervision, or keyword-based rules to assign soft labels, the approach enables domain-adapted word representations even when large manually annotated corpora are unavailable.

Word embedding with noisy/programmatic labels

Mikolov, T., Sutskever, I., Chen, K., Corrado, G., & Dean, J. (2013). Distributed representations of words and phrases and their compositionality. Advances in Neural Information Processing Systems, 26.

Ratner, A. J., De Sa, C. M., Wu, S., Selsam, D., & Re, C. (2016). Data programming: Creating large training sets, quickly. Advances in Neural Information Processing Systems, 29.


Web of Science Database

WoS
ISI Web of Science
Clarivate Analytics

Institute for Scientific Information (ISI), now Clarivate Analytics

Web of Science (WoS) is the oldest and most established multidisciplinary citation database, maintained by Clarivate Analytics since 1964. It indexes over 21,000 peer-reviewed journals, conference proceedings, and books across sciences, social sciences, and humanities. WoS provides researchers, librarians, and administrators with comprehensive citation tracking, publication metrics, and research evaluation tools essential for literature review, impact assessment, and research strategy.

Clarivate Analytics. (2024). Web of Science Core Collection. Retrieved from https://clarivate.com/webofsciencegroup/solutions/web-of-science-core-collection/

Garfield, E. (1955). Citation indexes for science: A new dimension of bibliographic information utilization and management. Science, 122(3159), 108-111.

Clarivate Analytics. (2023). Journal Citation Reports Methodology. https://clarivate.com/webofsciencegroup/essays/journal-citation-reports-methodology/

scopus-database impact-factor journal-citation-reports h-index scimago-journal-rank


Web Scraping

Web Scraping for Research Data Collection

web harvesting
screen scraping
web crawling
automated data extraction

Early internet practitioners; systematised in research contexts from the late 1990s onward

Web scraping is a computational data collection technique in which software automatically retrieves and extracts structured or semi-structured content from websites. Widely used in social science, computational linguistics, economics, and information science, it enables researchers to assemble large datasets from publicly accessible web sources — such as news archives, social media platforms, government portals, and online marketplaces — that would be impractical to collect manually.

Automated digital data collection technique

HTML/XML web pages, structured and semi-structured online text, tables, images, metadata

Mitchell, R. (2018). Web Scraping with Python: Collecting More Data from the Modern Web (2nd ed.). O'Reilly Media.

api-based-data-collection sensor-data-collection document-collection online-survey content-analysis text-mining


WEBIRA

WEBIRA (WEighted Bi-directional Ideal Ratio Analysis) is a ranking multi-criteria decision-making (MCDM) method introduced by Krstović, S., Stević, Ž., Stjepanović, Ž., Tomić, V. in 2022. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Krstović, S., Stević, Ž., Stjepanović, Ž., Tomić, V. (2022). A new multi-criteria decision making method WEBIRA and its application in transport. Operational Research in Engineering Sciences: Theory and Applications

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


WEDBA

WEDBA (Weighted Euclidean Distance Based Approach) is a ranking multi-criteria decision-making (MCDM) method introduced by Dadelo, S., Turskis, Z., Zavadskas, E. K., Dadeliene, R. in 2014. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Distance-based with vector normalisation

Dadelo, S., Turskis, Z., Zavadskas, E. K., Dadeliene, R. (2014). Multi-criteria assessment and ranking system of sport team formation based on objective-measured values of criteria set. Expert Systems with Applications


Weed Density Mapping

Weed Distribution Mapping and Density Assessment

Weed mapping
Spatial weed survey
Weed sampling

Weed Density Mapping is a spatial survey pipeline for measuring and mapping weed distributions across fields to support targeted herbicide application and management decisions. Developed by Gerhards, Christensen, and others in precision agriculture (2000s), this method combines field sampling or remote sensing with geostatistics to create weed pressure maps, enabling variable-rate control strategies.

Gerhards, R., & Christensen, S. (2003). Real-time weed detection, decision making and patch spraying in maize, sugarbeet, winter wheat and winter barley. Weed Research, 43(6), 385-392.

Visser, S. M., Sterk, G., & Rieger, W. (2003). Seasonal variability of saharan dust and its relation to vegetation cover in drylands. Journal of Geophysical Research, 110, D04302.

precision-agriculture-ndvi crop-growth-simulation pesticide-efficacy-trial crop-yield-estimation nitrogen-use-efficiency


Weibull Diameter Distribution

Weibull distribution
size-class distribution

The Weibull diameter distribution is a flexible three-parameter probability model used to describe the size-class distribution (proportion of trees by diameter class) in forest stands. Introduced by Bailey and Dell in 1973, the Weibull function provides an excellent fit to observed diameter distributions across diverse forest types and management histories. It is widely used in growth simulators, yield models, and forest inventory analysis because it can capture a variety of distribution shapes (right-skewed, near-normal, and even multi-modal) with just three parameters.

Bailey, R. L., & Dell, T. R. (1973). Quantifying diameter distributions with the Weibull function. Forest Science, 19(2), 97–104.

Rennolls, K., Geary, D. N., & Rollinson, T. J. (1985). Characterizing diameter distributions by the use of the Weibull distribution. Forestry, 58(1), 57–66.


Weibull Regression

Weibull Regresyonu — Parametrik Hayatta Kalma

Weibull regression is a fully parametric survival model, formalised by Kalbfleisch and Prentice, that assumes survival times follow a Weibull distribution. A shape parameter controls whether the hazard increases, decreases, or remains constant over time, while covariates shift the scale of the distribution to express how predictors affect survival.

Fully parametric survival regression model

Kalbfleisch, J. D. & Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data (2nd ed.). Wiley.

kaplan-meier cox-ph fine-gray-competing-risks bayesian-survival power-analysis-survival


Weight and Balance

Weight and balance analysis is the process of determining the total weight of an aircraft and the location of its center of gravity (CG) throughout its operational envelope. Essential for aircraft safety and performance, weight and balance ensures that the CG remains within allowable limits (forward and aft) to maintain stable flight and controllability. Regulatory certification requires comprehensive weight and balance documentation for every aircraft configuration.

Federal Aviation Administration (2017). Airplane Weight and Balance Control. Advisory Circular AC 23-8B-1C.

Raymer, D. P. (1992). Aircraft Design: A Conceptual Approach (2nd ed.). American Institute of Aeronautics and Astronautics.

Nicolai, L. M., & Carichner, G. E. (2010). Fundamentals of Aircraft and Airship Design, Volume 1: Aircraft Design (Rev. ed.). American Institute of Aeronautics and Astronautics.


WBIS

The Weight Bias Internalization Scale is an 11-item self-report instrument designed to measure the degree to which individuals with overweight or obesity internalize negative weight-based societal stereotypes and apply them to themselves. Developed by Durso and Latner in 2008, the WBIS measures self-directed weight stigma—the belief that one is inferior, lazy, or undesirable due to body weight. The WBIS is widely used in obesity research, psychological intervention studies, and health behavior research examining the impact of weight stigma on weight-related outcomes and mental health.

Ratz, T., & Miller, R. L. (2016). The Weight Bias Internalization Scale: Validation in a multiplex platform sample. Body Image, 16, 29-38.

Durso, L. E., & Latner, J. D. (2016). Understanding self-directed stigma: Development of the Weight Bias Internalization Scale. Obesity, 16(S2), 80-86.

body-weight-image-satisfaction nutrition-self-efficacy-scale intuitive-eating-scale dutch-eating-behavior-questionnaire food-neophobia-scale


WEIGHT-SENSITIVITY

WEIGHT-SENSITIVITY (Weight Sensitivity Analysis — Stability intervals for criterion weights) is a ranking multi-criteria decision-making (MCDM) method introduced by Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M. in 2004. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Robustness diagnostic — weight stability intervals

Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M. (2004). Sensitivity Analysis in Practice. Wiley, Chichester


Weighted Betweenness Centrality

Weighted Betweenness Centrality (Geodesic Path-Count on Edge-Weighted Graphs)

WBC
weighted shortest-path betweenness
edge-weighted betweenness
geodesic betweenness (weighted)

Opsahl, T.; Agneessens, F.; Skvoretz, J. (extending Freeman 1977 and Brandes 2001)

Weighted Betweenness Centrality extends Freeman's betweenness measure to edge-weighted graphs by routing shortest paths through a tunable transformation of edge weights. Nodes that sit on many high-value shortest paths receive high scores, identifying brokers and bridges in social, biological, and information networks where tie strength matters.

Edge-weighted directed or undirected graph (adjacency matrix or edge list with numeric weights)

Opsahl, T., Agneessens, F., & Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32(3), 245–251.

Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology, 25(2), 163–177.

betweenness-centrality weighted-degree-centrality weighted-closeness-centrality weighted-eigenvector-centrality social-network-analysis weighted-social-network-analysis


Weighted Closeness Centrality

Weighted Closeness Centrality (Opsahl Generalized Closeness)

weighted closeness
generalized closeness centrality
WCC
distance-weighted closeness

Opsahl, T.; Agneessens, F.; Skvoretz, J.

Weighted closeness centrality extends the classic closeness measure to networks where edges carry numerical weights — such as frequency, strength, or cost — by incorporating those weights into shortest-path distances. Nodes that can reach others quickly along strong or efficient connections receive higher scores, making it a richer indicator of information-spreading potential than its binary counterpart.

Weighted undirected or directed network (adjacency matrix with edge weights)

Opsahl, T., Agneessens, F. & Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32(3), 245–251.

closeness-centrality weighted-degree-centrality weighted-betweenness-centrality eigenvector-centrality weighted-eigenvector-centrality weighted-social-network-analysis


Weighted Community Detection

Weighted Community Detection in Networks

community detection on weighted networks

Weighted community detection identifies densely connected groups — communities — in networks where edges carry numeric strengths (weights). By incorporating edge weights into the modularity function, it reveals structure that binary adjacency alone would miss: two nodes connected by a strong tie are treated as more similar than two nodes linked by a weak one. The Louvain algorithm is the dominant practical implementation.

Weighted adjacency matrix / edge-list with numeric weights

Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10), P10008.

Newman, M. E. J. (2004). Analysis of weighted networks. Physical Review E, 70(5), 056131.

modularity-analysis weighted-modularity-analysis community-detection social-network-analysis weighted-social-network-analysis multiplex-network-analysis


Weighted Degree Centrality

Weighted Degree Centrality (Node Strength in Weighted Networks)

node strength
strength centrality
weighted node degree
WDC

Barrat, A.; Barthélemy, M.; Pastor-Satorras, R.; Vespignani, A.

Weighted degree centrality — also called node strength — extends the classic degree centrality measure to networks whose edges carry numeric weights. Instead of simply counting a node's connections, it sums the weights of all edges incident to that node, capturing both the volume and the intensity of a node's ties in a single, interpretable score.

Centrality measure for weighted networks

Barrat, A., Barthélemy, M., Pastor-Satorras, R., & Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences, 101(11), 3747–3752.

Newman, M. E. J. (2010). Networks: An Introduction. Oxford University Press.

degree-centrality betweenness-centrality closeness-centrality eigenvector-centrality weighted-betweenness-centrality social-network-analysis


Weighted Ego Network Analysis

Weighted Ego Network Analysis (Tie-Strength-Aware Personal Network Analysis)

weighted personal network analysis
ego-centered weighted network analysis
weighted egonet analysis
tie-strength ego network analysis

Weighted ego network analysis examines the personal network of a focal actor (the ego) and incorporates tie strength — measured as interaction frequency, closeness, or resource exchange — as edge weights. By moving beyond simple presence or absence of a tie, it captures how much each relationship matters and how those varying strengths shape outcomes such as social support, information access, or influence.

Ego-centered network analysis with weighted ties

Personal network data with tie-strength ratings (survey, interaction logs, communication records)

Marsden, P. V. (2002). Egocentric and sociocentric measures of network centrality. Social Networks, 24(4), 407–422.

McCarty, C., Killworth, P. D., & Rennell, J. (2007). Impact of methods for reducing respondent burden on personal network structural measures. Social Networks, 29(2), 300–315.

ego-network-analysis social-network-analysis weighted-social-network-analysis degree-centrality weighted-degree-centrality betweenness-centrality


Weighted Eigenvector Centrality

Weighted Eigenvector Centrality (Spectral Prestige in Weighted Networks)

1987 (binary); 2010 (weighted generalization)

Bonacich, P. (binary); Opsahl, T. et al. (weighted extension)

Weighted eigenvector centrality extends the classic eigenvector centrality measure to graphs where edges carry numerical weights, scoring each node proportionally to the sum of its neighbors' scores multiplied by the connecting edge weights. Nodes score highly not just by having many connections but by being strongly linked to other influential nodes, making the measure sensitive to both tie strength and network position simultaneously.

Weighted adjacency matrix (non-negative edge weights)

Bonacich, P. (1987). Power and centrality: A family of measures. American Journal of Sociology, 92(5), 1170–1182.

eigenvector-centrality weighted-degree-centrality weighted-betweenness-centrality weighted-closeness-centrality weighted-pagerank degree-centrality


Weighted Exponential Random Graph Model

Weighted Exponential Random Graph Model (Valued-Edge ERGM)

W-ERGM
valued ERGM
weighted p-star model
valued exponential random graph model

The Weighted Exponential Random Graph Model (W-ERGM) extends the classic binary ERGM framework to networks whose edges carry quantitative values — such as frequency of contact, trade volume, or collaboration intensity. It models the entire valued-edge network as a probability distribution defined over all possible weighted graphs, enabling researchers to test whether structural patterns such as reciprocity, transitivity, or degree distribution arise beyond what chance alone would produce.

Krivitsky, P. N. (2012). Exponential-family random graph models for valued networks. Electronic Journal of Statistics, 6, 1100–1128.

Robins, G., Pattison, P., Kalish, Y., & Lusher, D. (2007). An introduction to exponential random graph (p*) models for social networks. Social Networks, 29(2), 173–191.

exponential-random-graph-model weighted-stochastic-block-model weighted-modularity-analysis weighted-social-network-analysis weighted-degree-centrality temporal-exponential-random-graph-model


Weighted F1

Weighted F1 computes the F1-score for each class and then takes a weighted average, where weights are proportional to the number of samples in each class (support). It provides a middle ground between macro and micro-averaging.

Powers, D. M. (2011). Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness and Correlation. Journal of Machine Learning Technologies, 2(1), 37-63.

Sokolova, M., Japkowicz, N., & Szpakowicz, S. (2006). Beyond Accuracy, F-Score and ROC: a Family of Discriminant Measures for Performance Evaluation. AI 2006, 4013, 1015-1021.


Weighted Knowledge Graph Analysis

Weighted Knowledge Graph Analysis (Weight-Aware Structural and Semantic Network Analysis)

WKGA
weighted KG analysis
confidence-weighted knowledge graph
weighted semantic network analysis

Hogan et al. and the broader knowledge graph community

Weighted Knowledge Graph Analysis extends standard knowledge graph methods by assigning numerical weights — such as confidence scores, co-occurrence frequencies, or relation strengths — to edges between entities. These weights allow analysts to prioritise high-confidence triples, find the most influential paths, and compute weight-aware centrality and community structure in large structured knowledge bases.

Weighted directed or undirected graphs with typed relations and confidence/frequency scores

Hogan, A., Blomqvist, E., Cochez, M., d'Amato, C., Melo, G., Gutierrez, C., Kirrane, S., Gayo, J. E. L., Navigli, R., Neumaier, S., Ngomo, A. N., Polleres, A., Rashid, S. M., Rula, A., Schmelzeisen, L., Sequeda, J., Staab, S., & Zimmermann, A. (2021). Knowledge Graphs. ACM Computing Surveys, 54(4), 1–37.

Wang, Q., Zhang, F., Liu, Z., & Sun, M. (2017). Knowledge Graph Embedding by Translating on Hyperplanes. In Proceedings of the AAAI Conference on Artificial Intelligence, 28(1).

knowledge-graph-analysis weighted-network-diffusion-analysis weighted-betweenness-centrality weighted-eigenvector-centrality multiplex-network-analysis weighted-modularity-analysis


Weighted Least Squares

WLS
weighted regression
heteroscedasticity-corrected OLS
variance-weighted least squares

Weighted Least Squares is a generalization of Ordinary Least Squares (OLS) regression that assigns each observation a weight inversely proportional to its error variance, thereby down-weighting high-variance data points and up-weighting precise ones. Introduced in its general matrix form by Alexander Craig Aitken in 1935, WLS is the canonical remedy when heteroscedasticity is present and the error variance structure is known or can be reliably estimated.

BLUE under known heteroscedastic error structure

Known or estimable error variance structure

Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.

Greene, W. H. (2012). Econometric Analysis (7th ed.). Pearson Education.

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis (5th ed.). Wiley.

ordinary-least-squares generalized-least-squares feasible-generalized-least-squares heteroscedasticity-tests robust-regression linear-regression


Weighted Modularity Analysis

Weighted Modularity Analysis (Q-weighted community structure detection)

weighted modularity
weighted Q optimization
weighted network community detection
strength-based modularity

Weighted modularity analysis extends the classical Newman-Girvan modularity measure to networks where edges carry numeric strengths (frequencies, intensities, costs). By replacing binary adjacency with tie weights, it finds community partitions that reflect how densely interconnected subgroups are relative to what is expected under a weighted null model, yielding more nuanced groupings than unweighted approaches on data where edge strength varies meaningfully.

Community structure optimization on weighted graphs

Weighted adjacency matrix / edge-list with numeric tie strengths

Newman, M. E. J. (2006). Modularity and community structure in networks. Proceedings of the National Academy of Sciences, 103(23), 8577–8582.

modularity-analysis weighted-community-detection weighted-social-network-analysis exponential-random-graph-model betweenness-centrality weighted-betweenness-centrality


Weighted Multiplex Network Analysis

Weighted Multiplex Network Analysis (Multi-Layer Network Analysis with Edge Weights)

weighted multi-relational network analysis

Weighted multiplex network analysis studies systems in which the same set of actors are connected through multiple types of relationships simultaneously, and each relationship carries a quantitative strength or frequency. By capturing both the variety and the intensity of ties across layers, it reveals patterns invisible to single-layer or unweighted network approaches.

Weighted multi-relational adjacency matrices

Battiston, F., Nicosia, V., & Latora, V. (2014). Structural measures for multiplex networks. Physical Review E, 89(3), 032804.

Kivela, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014). Multilayer networks. Journal of Complex Networks, 2(3), 203-271.

multiplex-network-analysis weighted-network-diffusion-analysis multilayer-network-analysis weighted-community-detection weighted-betweenness-centrality weighted-eigenvector-centrality


Weighted Network Diffusion Analysis

WNDA
weighted diffusion process
edge-weighted spreading analysis
weighted information diffusion

Weighted Network Diffusion Analysis models how information, influence, disease, or resources spread through a network whose edges carry quantitative strength values. By letting tie weights govern transition probabilities, the method produces more realistic spreading dynamics than binary-edge diffusion, revealing which high-traffic pathways dominate propagation in social, biological, and information networks.

Weighted adjacency matrices, relational tie-strength data

Barrat, A., Barthelemy, M., Pastor-Satorras, R., & Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences, 101(11), 3747–3752.

Newman, M. E. J. (2004). Analysis of weighted networks. Physical Review E, 70(5), 056131.

network-diffusion-analysis weighted-social-network-analysis weighted-betweenness-centrality weighted-pagerank multiplex-network-analysis weighted-community-detection


Weighted PageRank

WPR
weighted page rank
edge-weighted PageRank
strength-based PageRank

Weighted PageRank extends the classic PageRank algorithm to networks where edges carry different strengths or frequencies, distributing importance proportionally to both incoming and outgoing edge weights rather than treating all links equally. This makes it substantially more informative than binary PageRank in any network where connection strength matters.

Weighted directed or undirected networks

Xing, W., & Ghorbani, A. (2004). Weighted PageRank algorithm. Proceedings of the Second Annual Conference on Communication Networks and Services Research (CNSR '04), pp. 305–314. IEEE.

degree-centrality eigenvector-centrality betweenness-centrality weighted-degree-centrality weighted-eigenvector-centrality social-network-analysis


Weighted Quota Sampling

quota sampling with weighting
weighted quota survey
post-weighted quota sampling
quota sample weighting

Derived from quota sampling (mid-20th century market research) combined with survey weighting theory (Kalton, 1983)

Weighted quota sampling combines quota sampling — recruiting a set number of respondents matching pre-specified demographic cells — with post-collection statistical weighting that adjusts each respondent's contribution to match known population proportions. The result is a non-probability design with a bias-correction mechanism, widely used in market research, political polling, and applied social surveys when probability sampling is impractical but representativeness remains a goal.

Non-probability sampling with post-collection weight adjustment

Categorical/continuous survey data; requires known population proportions for weighting variables

Kalton, G. (1983). Introduction to Survey Sampling. Sage Publications.

Kalton, G., & Flores-Cervantes, I. (2003). Weighting methods. Journal of Official Statistics, 19(2), 81–97.

quota-sampling weighted-sampling stratified-sampling proportional-quota-sampling systematic-sampling simple-random-sampling


Weighted Sampling

probability proportional to size sampling

1940s–1952 (formalized in large-scale government survey work and the Horvitz-Thompson estimator)

Morris H. Hansen, William N. Hurwitz; D. G. Horvitz and D. J. Thompson (theoretical framework)

Weighted sampling is a probability-based design in which units are selected with unequal probabilities proportional to a known auxiliary measure of size or importance. Sampling weights — the inverse of inclusion probabilities — are applied during analysis so that each sampled unit correctly represents the population units it stands for. The approach underpins large-scale government, health, and social surveys where simple random sampling would be inefficient.

Any quantitative or categorical survey data; requires auxiliary size variable

Cochran, W. G. (1977). Sampling Techniques (3rd ed.). John Wiley & Sons.

Horvitz, D. G., & Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47(260), 663-685.

simple-random-sampling stratified-sampling cluster-sampling systematic-sampling multistage-sampling proportional-stratified-sampling


Weighted Snowball Sampling

weight-adjusted chain-referral sampling
probability-weighted snowball sampling
WSS
weighted referral sampling

Douglas D. Heckathorn (formal probability-weighted variant)

Weighted snowball sampling is a chain-referral technique in which participants recruit peers from a hidden or hard-to-reach population, and differential inclusion probabilities are estimated and corrected through statistical weights. Unlike basic snowball sampling, the weighting step allows approximately unbiased population estimates, bridging the gap between convenience-driven recruitment and probability-based inference.

Survey or interview data from hard-to-reach or hidden populations

Heckathorn, D. D. (1997). Respondent-driven sampling: A new approach to the study of hidden populations. Social Problems, 44(2), 174–199.

Salganik, M. J., & Heckathorn, D. D. (2004). Sampling and estimation in hidden populations using respondent-driven sampling. Sociological Methodology, 34(1), 193–240.

snowball-sampling respondent-driven-sampling weighted-sampling adaptive-snowball-sampling purposive-sampling network-sampling


Weighted Social Network Analysis

Weighted Social Network Analysis (Tie-Strength SNA)

Weighted SNA
valued network analysis
tie-strength network analysis
weighted graph analysis

Weighted Social Network Analysis extends classical SNA by assigning numeric values — weights — to ties between actors, capturing tie strength, interaction frequency, or resource flow. Rather than treating all connections as equal, it reveals who holds privileged positions by virtue of the intensity, not merely the existence, of their relationships.

Relational data with numeric edge weights

Barrat, A., Barthélemy, M., Pastor-Satorras, R., & Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences, 101(11), 3747–3752.

Opsahl, T., Agneessens, F., & Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32(3), 245–251.

social-network-analysis degree-centrality betweenness-centrality weighted-degree-centrality weighted-betweenness-centrality modularity-analysis


Weighted Stochastic Block Model

W-SBM
weighted SBM
weighted block model
weighted community detection via SBM

The Weighted Stochastic Block Model (W-SBM) extends the classical stochastic block model to networks whose edges carry numerical weights. By positing that edge weights between node pairs arise from distributions that depend on the block memberships of those nodes, it simultaneously infers a partition of nodes into communities and a set of block-to-block weight parameters — recovering structure invisible to unweighted methods.

Weighted adjacency matrices; edge weights (counts, continuous, or binary)

Aicher, C., Jacobs, A. Z., & Clauset, A. (2014). Learning latent block structure in weighted networks. Journal of Complex Networks, 3(2), 221–248.

Nowicki, K., & Snijders, T. A. B. (2001). Estimation and prediction for stochastic blockstructures. Journal of the American Statistical Association, 96(455), 1077–1087.

stochastic-block-model weighted-modularity-analysis weighted-community-detection weighted-exponential-random-graph-model modularity-analysis weighted-social-network-analysis


Weighted Stratified Sampling

stratified sampling with weights
design-weighted stratified sampling
post-stratification weighting
WSS

Weighted stratified sampling divides a population into non-overlapping strata and draws a probability sample from each stratum, then attaches a design weight to every selected unit so that estimates correctly represent the full population. Weights compensate for unequal selection probabilities that arise from disproportionate stratum allocations, non-response, or frame imperfections, making the procedure the backbone of most large-scale national and international surveys.

Quantitative (survey, census, administrative data)

Kish, L. (1965). Survey Sampling. John Wiley & Sons.

stratified-sampling proportional-stratified-sampling disproportional-stratified-sampling simple-random-sampling multistage-sampling cluster-sampling


Weighted Systematic Sampling

William G. Cochran (systematic and weighted probability sampling theory)

Weighted systematic sampling selects units at equal spacing along a cumulative-weight axis rather than along a simple list index. By ordering the population and accumulating auxiliary size or importance weights before applying a fixed sampling interval, it combines the operational simplicity of systematic sampling with the efficiency gains of probability-proportional-to-size selection — giving larger or more important units a higher probability of inclusion while still visiting every part of the ordered frame.

Population lists or frames with auxiliary size or weight variables

Cochran, W. G. (1977). Sampling Techniques (3rd ed.). Wiley.

Lohr, S. L. (2021). Sampling: Design and Analysis (3rd ed.). CRC Press / Chapman & Hall.


Weighted Temporal Network Analysis

Weighted Temporal Network Analysis (Time-Varying Weighted Graph Analysis)

WTNA
weighted time-varying network analysis
weighted dynamic network analysis
weighted evolving network analysis

Holme, P. & Saramaki, J. (temporal networks); Barrat et al. (weighted networks)

Weighted temporal network analysis studies networks whose edges carry numerical weights — representing interaction strength, frequency, or intensity — and whose structure changes over time. It combines the time-varying perspective of temporal network analysis with the quantitative precision of weighted graph metrics, revealing not only when connections exist but how strong they are at each moment.

Time-stamped weighted edge lists (interaction logs, contact sequences)

Holme, P. & Saramaki, J. (2012). Temporal networks. Physics Reports, 519(3), 97–125.

Barrat, A., Barthelemy, M., Pastor-Satorras, R. & Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences, 101(11), 3747–3752.

temporal-network-analysis weighted-social-network-analysis multiplex-network-analysis weighted-community-detection network-diffusion-analysis weighted-network-diffusion-analysis


Weighted Two-Mode Network Analysis

Weighted Two-Mode (Bipartite) Network Analysis

weighted bipartite network analysis
valued two-mode network analysis
weighted affiliation network analysis
W2MNA

1997 (two-mode); weighted extensions 2000s

Weighted two-mode network analysis examines bipartite graphs in which two distinct node sets — such as actors and events, authors and papers, or species and habitats — are connected by edges carrying numerical weights that capture the strength, frequency, or intensity of each affiliation. Incorporating weights provides substantially richer structural insights than unweighted bipartite analysis.

Weighted bipartite (two-mode) adjacency or incidence matrices

Borgatti, S. P., & Everett, M. G. (1997). Network analysis of 2-mode data. Social Networks, 19(3), 243–269.

Newman, M. E. J., Strogatz, S. H., & Watts, D. J. (2001). Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64(2), 026118.

two-mode-network-analysis weighted-social-network-analysis modularity-analysis weighted-modularity-analysis multiplex-network-analysis knowledge-graph-analysis


Weighted Typical Case Sampling

probability-weighted typical case selection

1990s–2000s (as a mixed-methods extension)

Derived from Patton's typical case sampling (1990) combined with classical survey weighting principles

Weighted typical case sampling combines the purposive logic of typical case selection — choosing cases that represent the modal, average, or most common profile of a population — with post-selection probability weighting. The result is a sample that is both substantively representative (cases reflect the norm) and statistically corrected for differential selection probabilities or population structure. It is used in mixed-methods and survey research where depth of typical examples matters alongside inferential accuracy.

Purposive sampling with probability weighting

Mixed (qualitative cases selected purposively; quantitative weights applied)

Patton, M. Q. (2002). Qualitative Research and Evaluation Methods (3rd ed.). Sage. pp. 236–238 (typical case sampling).

Kalton, G. (1983). Introduction to Survey Sampling. Sage. (weighting and probability adjustment principles).

typical-case-sampling purposive-sampling weighted-sampling maximum-variation-sampling stratified-sampling quota-sampling


WEIGHTED-VOTING

WEIGHTED-VOTING (Weighted Voting — Weighted positional aggregation of multiple rankings) is a ranking multi-criteria decision-making (MCDM) method introduced by Arrow, K. J. in 1951. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Social choice — weighted positional voting rule

Arrow, K. J. (1951). Social Choice and Individual Values. Wiley, New York


Welch ANOVA

Welch's F-test
heteroscedastic one-way ANOVA
Welch ANOVA — Heterojen Varyans ANOVA

Welch ANOVA is a parametric hypothesis test that compares the means of three or more independent groups when their variances are not equal. Introduced by B. L. Welch in 1951, it replaces classic one-way ANOVA whenever the homogeneity-of-variance assumption fails, while still requiring approximately normal data.

Parametric mean comparison (heteroscedastic)

k − 1 numerator; adjusted denominator df

Welch, B.L. (1951). On the Comparison of Several Mean Values. Biometrika, 38(3/4), 330–336.

one-way-anova brown-forsythe-test kruskal-wallis games-howell welch-t-test


Welch t-test

unequal variances t-test
Welch-Satterthwaite t-test
Welch t-Testi (Eşit Olmayan Varyans)

Welch's t-test is a parametric hypothesis test that compares the means of two independent groups without assuming their variances are equal. It was introduced by B. L. Welch in 1947 as a more robust generalization of Student's two-sample test for situations where the two groups have different spread.

Parametric mean comparison (unequal variances)

Welch, B. L. (1947). The generalization of Student's problem when several different population variances are involved. Biometrika, 34(1/2), 28–35.

independent-t-test paired-t-test mann-whitney-u one-way-anova levene-test


Well Log Analysis

wireline logging
borehole logging
petrophysical analysis

Well log analysis is the systematic examination of measurements recorded by instruments lowered into a borehole to characterize subsurface lithology, fluid content, and petrophysical properties. Originating in the 1940s, this method has become indispensable for petroleum exploration, groundwater assessment, and engineering geology. Well logs provide direct depth-correlated data that anchor interpretation of seismic surveys and constrain reservoir models.

Asquith, G. B., & Gibson, C. R. (2004). Basic Well Log Analysis (2nd ed.). American Association of Petroleum Geologists.

Rider, M., & Kennedy, M. (2002). The Geological Interpretation of Well Logs (2nd ed.). Rider-French Consulting Ltd.

Schlumberger Limited. (2019). Petrophysics: A Practical Guide. Schlumberger Oilfield Services.

seismic-reflection-interpretation petrographic-analysis stratigraphic-correlation geologic-mapping geochronological-dating


Wells Score for DVT

Wells Score for Deep Vein Thrombosis Risk Assessment

The Wells score, developed by Wells et al. in 1994, is a clinical prediction rule that stratifies patients into low, intermediate, or high pretest probability of deep vein thrombosis (DVT). It combines seven clinical features to guide diagnostic testing decisions and reduce unnecessary imaging in suspected DVT patients.

Venous thromboembolism risk stratification

Wells, P. S., Hirsh, J., Anderson, D. R., et al. (1994). A simple clinical model for the diagnosis of deep-vein thrombosis combined with impedance plethysmography. Archives of Internal Medicine, 154(13), 1541-1546.

Wells, P. S., Anderson, D. R., Rodger, M., et al. (2003). Evaluation of D-dimer in the diagnosis of suspected deep-vein thrombosis. New England Journal of Medicine, 349(13), 1227-1235.


WENSLO

WENSLO (WEight deNomination based on Slope coefficient for objective weighting) is a weight objective multi-criteria decision-making (MCDM) method introduced by Pamucar, D., Ecer, F., Gligorić, Z., Gligorić, M., Deveci, M. in 2024. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Weight_Objective (envelope/slope ratio of accumulation polyline)

Pamucar, D., Ecer, F., Gligorić, Z., Gligorić, M., Deveci, M. (2024). A Novel WENSLO and ALWAS Multicriteria Methodology and Its Application to Green Growth Performance Evaluation. IEEE Transactions on Engineering Management

ahpsort aploco aras aroman artasi cobra cocoso codas


WGM

WGM (Weighted Geometric Mean) is a aggregation multi-criteria decision-making (MCDM) method introduced by Aczél, J. Saaty, T. L. in 1983. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Mean-based aggregation operator — multiplicative

Aczél, J., Saaty, T. L. (1983). Procedures for synthesizing ratio judgements. Journal of Mathematical Psychology


Whale Optimization Algorithm

WOA
Balina Optimizasyon Algoritması (WOA)
bubble-net attacking method

The Whale Optimization Algorithm (WOA) is a swarm-based metaheuristic introduced by Mirjalili and Lewis in 2016. It models the bubble-net hunting strategy of humpback whales, in which a group of whales spirals around prey while gradually tightening the encirclement. The algorithm balances global exploration and local exploitation through a small set of parameters and has become widely used in continuous engineering optimisation problems.

Bubble-net hunting behaviour of humpback whales

Population size, maximum iterations, logarithmic spiral constant b

No minimum; population size typically 20–50 agents

Mirjalili, S. & Lewis, A. (2016). The Whale Optimization Algorithm. Advances in Engineering Software, 95, 51-67.

Chakraborty, S. et al. (2023). A Comprehensive Review of the Whale Optimization Algorithm: Modifications, Variants, and Applications. Artificial Intelligence Review.

particle-swarm-optimization grey-wolf-optimizer genetic-algorithm simulated-annealing bayesian-optimization


White Test

White's general heteroskedasticity test
White değişen varyans testi

The White test, introduced by Halbert White in 1980, is a general test for heteroskedasticity that makes no assumption about its functional form. It regresses the squared OLS residuals on the regressors, their squares, and their cross-products, so it can detect heteroskedasticity related to any of these terms. The same 1980 paper introduced the heteroskedasticity-consistent ('White') standard errors that are the standard remedy when the test rejects.

Homoskedastic errors (constant variance)

White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48(4), 817–838.


WHM

WHM (Weighted Harmonic Mean) is a aggregation multi-criteria decision-making (MCDM) method introduced by Bullen, P. S. Mitrinović, D. S. Vasić, P. M. in 1988. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Mean-based aggregation operator — harmonic

Bullen, P. S., Mitrinović, D. S., Vasić, P. M. (1988). Means and Their Inequalities. D. Reidel Publishing (Springer)


WHO-5 Well-Being Index

World Health Organization Well-Being Index

The WHO-5 is a 5-item screening instrument measuring current well-being over the past two weeks. Developed by the World Health Organization in 1998, it assesses positive mental health states and is widely used in both research and clinical practice to identify individuals at risk for depression. Its brevity, validity, and cross-cultural acceptance make it a standard tool in primary care and epidemiological surveys worldwide.

World Health Organization (1998). Wellbeing measures in primary health care: the DepCare project. WHO regional publications European series, 69.

flourishing-scale meaning-in-life-questionnaire perma-scale mindfulness-attention-awareness


WHODAS 2.0

World Health Organization Disability Assessment Schedule 2.0

WHODAS 2.0 is a standardized, WHO-developed instrument that measures disability and functioning across six core life domains in any population aged 18 and above. Introduced in 2010, it operationalizes the biopsychosocial model of disability using the International Classification of Functioning (ICF) framework, making it applicable to chronic disease, physical injury, mental health, and aging contexts.

World Health Organization. (2010). Measuring Health and Disability: Manual for WHO Disability Assessment Schedule (WHODAS 2.0). WHO Publications.

Ustün, T. B., Kostanjsek, N., Chatterji, S., & Rehm, J. (2010). Measuring health and disability: Manual for the World Health Organization Disability Assessment Schedule (WHODAS 2.0). WHO.

community-integration-questionnaire impact-participation-autonomy assessment-life-habits participation-measure-post-acute craig-handicap-assessment


WHOQOL-BREF

World Health Organization Quality of Life Brief Version

WHOQOL-BREF Questionnaire
WHO Quality of Life-BREF

World Health Organization Quality of Life Group

The WHOQOL-BREF is the brief version of the World Health Organization's quality of life assessment, developed by the WHO Quality of Life Group and published in 1998. It measures quality of life across physical, psychological, social, and environmental domains in a single 26-item self-report questionnaire. It has become the primary quality of life instrument in global health research and clinical practice.

Multidimensional quality of life assessment

The WHOQOL Group. (1998). Development of the World Health Organization WHOQOL-BREF quality of life assessment. Psychological Medicine, 28(3), 551–558.

Skevington, S. M., Lotfy, M., & O'Connell, K. A. (2004). The World Health Organization's WHOQOL-BREF quality of life assessment: Psychometric properties and results of the international field trial. Quality of Life Research, 13(2), 299–310.

The WHOQOL Group. (1996). WHOQOL-BREF: Introduction, administration, scoring and generic version of the assessment. Mental Health Programme, WHO.


Wiener Filter

Wiener Optimal Filter
Kolmogorov-Wiener Filter
Mean-Square Optimal Filter

The Wiener filter is an optimal linear filter that minimizes mean-square error between the desired signal and the filter output given knowledge of signal and noise statistics. Developed by Norbert Wiener in 1949, it provides the theoretical foundation for optimal filtering and remains the benchmark against which all other linear filtering methods are compared.

Wiener, N. (1949). Extrapolation, Interpolation, and Smoothing of Stationary Time Series. John Wiley & Sons.

Haykin, S. (2002). Adaptive Filter Theory (4th ed.). Prentice Hall.

adaptive-lms-filter kalman-filter-signal matched-filter iir-filter-design


Wilcoxon signed-rank test

Wilcoxon matched-pairs signed-rank test
signed-rank test
Wilcoxon İşaretli Sıra Testi

The Wilcoxon signed-rank test is the nonparametric alternative to the paired t-test, comparing two related measurements on the same subjects to decide whether their typical difference is zero. It was introduced by Frank Wilcoxon in 1945 and works on continuous or ordinal data without assuming normality.

Normal approximation of the signed-rank statistic for large samples

Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83.

paired-t-test sign-test mann-whitney-u kruskal-wallis


Wild Bootstrap

wild bootstrap
wild cluster bootstrap
Wu-Liu resampling
Wild Bootstrap

Wu (1986); refined by Davidson & Flachaire (2008)

The wild bootstrap is a resampling method for regression models with heteroscedastic errors, introduced by Wu (1986) and refined by Davidson and Flachaire (2008). It builds a bootstrap distribution by rescaling each fitted residual with a random sign, so that standard errors and confidence intervals stay valid when the error variance is not constant or the data are clustered.

Bootstrap distribution from sign-perturbed residuals

heteroscedasticity and cluster structure

Wu, C. F. J. (1986). Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis. Annals of Statistics, 14(4), 1261-1295.

Davidson, R., & Flachaire, E. (2008). The Wild Bootstrap, Tamed at Last. Journal of Econometrics, 146(1), 162-169.

ols-regression bootstrap-inference block-bootstrap bayesian-bootstrap permutation-test


Willingness-to-Pay Estimation

Price Elasticity Analysis
Valuation Estimation
Monetary Value Elicitation

Willingness-to-Pay (WTP) estimation encompasses methods for quantifying the maximum price consumers are willing to pay for a product, service, or feature. Developed through advances in marketing research and behavioral economics, WTP estimation helps organizations set optimal prices, allocate marketing budgets, value product features, and understand customer value perception.

Wertenbroch, K., & Skiera, B. (1998). Measuring Consumers' Willingness to Pay at the Point of Purchase. Journal of Marketing Research, 35(4), 460-469.

Jedidi, K., Jagpal, S., & DeSarbo, W. S. (2003). A Stochastic Multidimensional Scaling Procedure for the Spatial Representation of Semantic Concepts. Journal of Marketing Research, 40(1), 72-85.

Backhaus, K., Erichson, B., & Plinke, W. (2016). Multivariate Analysis Methods and Applications (3rd ed.). Springer.

market-segmentation-analysis price-sensitivity-meter marketing-mix-modeling customer-lifetime-value brand-equity-measurement


Willingness to Pay in Health

Willingness to Pay (WTP) Assessment in Health Economics

WTP
contingent valuation
stated preference method

Carson & Louviere (stated preference/contingent valuation methods)

Willingness to pay (WTP) is an economic valuation method that elicits what individuals or society are willing to spend for a health benefit or to avoid a health risk. Rooted in contingent valuation (Carson & Louviere, 1980s), WTP is used to monetize health outcomes for cost-benefit analysis and to infer implicit cost-effectiveness thresholds from actual healthcare spending patterns. Unlike revealed preference (observing actual spending behavior), WTP uses stated preferences—surveys asking respondents: 'How much would you pay for this health improvement?'

Carson, R. T., & Louviere, J. J. (2011). A Common Nomenclature for Stated Choice Studies. In S. Hess & A. Daly (Eds.), Choice Modelling: The State of the Art and the State of Practice. Cheltenham: Edward Elgar.

Grosse, S. D. (2008). Assessing Cost-Effectiveness in Healthcare: History of the $50,000-per-Life-Year Benchmark. Health Care Management Science, 11(2), 176-182.

Drummond, M. F., Sculpher, M. J., Claxton, K., Stoddart, G. L., & Torrance, G. W. (2015). Methods for the Economic Evaluation of Health Care Programmes (4th ed.). Oxford: Oxford University Press.

cost-effectiveness-analysis cost-benefit-analysis quality-adjusted-life-year decision-analytic-modeling markov-model-health-economics


Windkessel Model

Windkessel Model of Arterial Hemodynamics

Elastic chamber model
Arterial compliance model
Lumped parameter model

The Windkessel model is a lumped-parameter representation of the arterial system that captures the pulsatile dynamics of blood flow and pressure using simple mechanical analogs (resistors and capacitors). Named after the German word for air chamber, it was formalized by Westerhof and colleagues in the late 1960s and remains fundamental to understanding arterial hemodynamics and blood pressure regulation.

Westerhof, N., Bosman, F., De Vries, N. C., & Noordergraaf, A. (1969). Analog studies of the human systemic arterial tree. Journal of Biomechanics, 2(2), 121-143.

Fung, Y. C. (1997). Biomechanics: Circulation (2nd ed.). Springer-Verlag.


Window DEA

Sliding-Window DEA
Temporal DEA
Rolling-Period DEA
Pencere VZA

Window Data Envelopment Analysis (Window DEA) is a non-parametric panel efficiency method that evaluates decision-making units (DMUs) over time by embedding each DMU's observations across a rolling temporal window into a single cross-sectional DEA problem. Introduced by Charnes, Clark, Cooper, and Golany in 1984, it enables longitudinal efficiency tracking without requiring a full panel, increasing discriminatory power by pooling observations across consecutive periods.

Charnes, A., Clark, C. T., Cooper, W. W., & Golany, B. (1984). A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the U.S. Air Forces. Annals of Operations Research, 2(1), 95–112.


WINGS

WINGS (Weighted Influence Non-linear Gauge System) is a ranking multi-criteria decision-making (MCDM) method introduced by Michnik, J. in 2013. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Influence network weighting + DEMATEL-style strength scoring

Michnik, J. (2013). Weighted Influence Non-linear Gauge System (WINGS) — An analysis method for the systems of interrelated components. European Journal of Operational Research


Winsorized Estimation

Winsorized Estimation of Location and Scale

winsorization
winsorized mean
Winsorize Edilmiş Tahmin

Dixon (1960); robust estimation tradition (Wilcox)

Winsorized estimation is a robust technique that reduces the influence of outliers by clamping the extreme percentiles of a distribution to a chosen threshold. Introduced by Dixon (1960) and developed in the robust-estimation tradition of Wilcox, it keeps every observation in the sample rather than discarding any.

Winsorized mean (tails pulled to percentile thresholds)

Dixon, W. J. (1960). Simplified Estimation from Censored Normal Samples. Annals of Mathematical Statistics, 31(2), 385-391.

Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press.

trimmed-mean-test mad-estimation robust-correlation permutation-test influence-diagnostics


WISP

WISP (Weighted Ideal Solution Point) is a ranking multi-criteria decision-making (MCDM) method introduced by Stanković, M., Stević, Ž., Das, D. K., Subotić, M., Pamučar, D. in 2020. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Ideal solution proximity (four score components)

Stanković, M., Stević, Ž., Das, D. K., Subotić, M., Pamučar, D. (2020). A new fuzzy MARCOS method for road traffic risk analysis. Mathematics

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


Wizard of Oz

WOz
Wizard of Oz Prototyping
Hidden Operator Simulation

The Wizard of Oz method is a prototyping and evaluation technique where users interact with what appears to be an automated system, but behind the scenes, a human operator (the wizard) controls the system's behavior. Developed by John Kelley in 1984, this method is especially valuable for exploring novel interaction paradigms (voice interfaces, AI assistants, gesture-based systems) before full implementation. By simulating future system capabilities, researchers gain insight into user expectations, mental models, and requirements without building the complex automation first.

Iterative design technique using hidden human operator to simulate future system behavior

Kelley, J. F. (1984). An iterative design methodology for user-friendly natural language office information applications. ACM Transactions on Information Systems, 2(1), 26–41.

Maulsby, D., Greenberg, S., & Mander, R. (1993). Prototyping an intelligent agent through Wizard of Oz. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 277–284).

think-aloud-protocol contextual-inquiry pluralistic-walkthrough retrospective-think-aloud


WOMAC Osteoarthritis Index

The Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) is a widely used patient-reported outcome measure designed to assess pain, stiffness, and physical function in patients with osteoarthritis of the hip or knee. Developed by Bellamy and colleagues in 1988, it has become the gold standard outcome measure in osteoarthritis clinical trials and practice.

Bellamy, N., Buchanan, W. W., Goldsmith, C. H., Campbell, J., & Stitt, L. W. (1988). Validation study of WOMAC: a health status instrument for measuring clinically important patient relevant outcomes to antirheumatic drug therapy in patients with osteoarthritis of the hip or knee. Journal of Rheumatology, 15(12), 1833–1840.

Bellamy, N. (1997). WOMAC: a 20-year experiential review of a patient-centered self-reported health status questionnaire. Journal of Rheumatology, 29(12), 2473–2476.

koos hoos oswestry-disability-index dash-outcome-measure


Wood Shrinkage

dimensional change
anisotropic shrinkage

Wood shrinkage is the dimensional change that occurs as wood loses moisture from green (freshly felled) to oven-dry condition. Wood shrinks anisotropically: tangentially (along growth rings) more than radially (from center to edge), and both more than longitudinally (along the grain). Measuring shrinkage percentages is essential for understanding wood drying behavior, predicting checking and warping, and selecting materials for applications sensitive to dimensional change (flooring, cabinetry, musical instruments).

ASTM D143-19. (2019). Standard test methods for small clear specimens of timber. ASTM International.

Skaar, C. (1988). Wood-Water Relations. Springer-Verlag.


Word Sense Disambiguation

WSD
sense tagging
Sözcük Anlamı Belirsizlik Giderme (WSD)

Word sense disambiguation (WSD) is the natural-language-processing task of choosing the correct meaning of a polysemous word from its context. Surveyed by Navigli (2009), it resolves which sense of a many-meaning word applies in a given sentence, improving the quality of information retrieval, machine translation, and question answering.

Output: Most likely sense label per ambiguous word in context

Navigli, R. (2009). Word Sense Disambiguation: A Survey. ACM Computing Surveys (CSUR), 41(2), Article 10, 1-69.

Mihalcea, R. (2006). Knowledge-Based Methods for Word Sense Disambiguation. Computational Linguistics.


word embeddings
skip-gram
continuous bag-of-words
Word2Vec Kelime Gömülmeleri

Word2Vec is a neural word-embedding technique introduced by Mikolov and colleagues in 2013 that maps each word in a text corpus to a dense numeric vector. Words that appear in similar contexts end up close together in the vector space, so the embeddings capture semantic similarity that can be measured arithmetically.

Output: Dense word vectors (typically 100-300 dimensions)

Input: Large unlabelled text corpus

Skip-gram / Continuous Bag-of-Words (CBOW)

Mikolov, T., Chen, K., Corrado, G. & Dean, J. (2013). Efficient Estimation of Word Representations in Vector Space.

glove-embeddings tf-idf document-clustering text-classification


Wordfish

Wordfish is a statistical model for scaling documents on latent dimensions, developed by Slapin and Proksch (2008). Unlike reference-based methods like Wordscores, Wordfish uses a Poisson generative model to jointly estimate word frequencies and document positions without requiring reference texts or manual annotation. It is particularly useful for estimating time-series changes in policy positions and can scale documents from multiple languages simultaneously.

Generative text model for dimension reduction

Slapin, J. B., & Proksch, S. O. (2008). A scaling model for estimating time-series party positions from texts. Journal of Politics, 70(3), 554-569.

Proksch, S. O., & Slapin, J. B. (2009). How to avoid pitfalls in statistical machine learning for social science. Political Analysis, 20(3), 343-357.

Benoit, K., Muhr, D., & Spirling, A. (2016). Crowd-sourced text analysis: Reproducible and distributed production of political data. American Political Science Review, 110(2), 278-295.


Wordscores

Michael Laver, Kenneth Benoit, John Garry

Wordscores is a text-based scaling method developed by Laver, Benoit, and Garry (2003) that estimates the policy positions of political actors based on word frequencies in their texts. By comparing word usage in reference texts of known positions with test texts, the method infers the latent political dimension of any document without requiring manual coding or training data.

Laver, M., Benoit, K., & Garry, J. (2003). Extracting policy positions from political texts using words as data. American Political Science Review, 97(2), 311-331.

Benoit, K., & Laver, M. (2012). The basic arithmetic of legislative decisions. Journal of Political Institutions and Political Economy, 1(1), 1-29.

Klemmensen, R., Hobolt, S. B., & Hansen, M. E. (2007). Estimating policy positions using political texts: A scaling approach. Electoral Studies, 26(4), 746-755.


Work Ability Index

Kaija Tuomi, Juhani Ilmarinen, Asko Jahkola, Leena Katajarinne, and Aune Tulkki

The Work Ability Index (WAI), developed by Tuomi and colleagues at the Finnish Institute of Occupational Health in 1998, is a validated self-assessment instrument measuring the ability to perform work. The WAI comprises seven dimensions: current work ability compared to lifetime best, work ability relative to job demands, number of diagnosed diseases, absenteeism, prognosis, mental resources, and productivity. It is widely used in occupational health surveillance, aging-workforce management, and return-to-work programs.

Tuomi, K., Ilmarinen, J., Jahkola, A., Katajarinne, L., & Tulkki, A. (1998). Work Ability Index (2nd edn). Helsinki: Finnish Institute of Occupational Health.

Ilmarinen, J. (2007). Work ability: past and present. International Journal of Environmental Research and Public Health, 13(1), 114.

job-demands-resources-scale perceived-stress-scale emotional-exhaustion-scale job-satisfaction-survey organizational-commitment-scale


Work Ability Questionnaire Extended

Ilmarinen, Tuomi, & Finnish Institute of Occupational Health

The Work Ability Index (WAI) measures workers' capacity to perform their current job given their health status, job demands, and life circumstances. Developed by Finnish occupational health researchers, the WAI captures the dynamic relationship between personal capacity (physical fitness, mental health, skills) and job demands, identifying workers at risk of sickness absence, work disability, and early retirement. The WAI is a leading indicator for occupational health intervention, used in occupational health surveillance, rehabilitation, and aging worker management.

Tuomi, K., Ilmarinen, J., Jahkola, A., Katajarinne, L., & Tulkki, A. (2006). Work Ability Index (2nd ed.). Finnish Institute of Occupational Health.

Ilmarinen, J. (2007). Work ability: A comprehensive concept for occupational health research and practice. Scand J Work Environ Health, 35(5), 1–5.