libscientific: A Powerful C Library for Multivariate Analysis

Libscientific is a C framework for multivariate and other statistical analysis written to be quasi-completely independent of common and well-established calculus libraries, except for the lapack library, which is used only to calculate left eigenvectors and eigenvalues.

The main goals of libscientific are:

1. To provide a simple and tiny framework for multivariate analysis that can be used not only in regular computers but also in embedded systems
2. Create a robust library of multivariate algorithms for any research and industrial application

Currently libscientific is able to compute:

• Multivariate analysis

  • Principal Component Analysis (PCA) NIPALS algorithm) [1]
  • Partial Least Squares (PLS) NIPALS algorithm [1]
  • Consensus PCA (CPCA) NIPALS algorithm [7]
  • Multiple Linear Regression (MLR) Ordinary least squares algorithm
  • Unfold PCA (UPCA) [2]
  • Unfold PLS (UPLS) [2]
  • Fisher LDA

• Clustering

  • K-means++ (David Arthur modification) [3]
  • Hierarchical clustering

• Object/Instance selection

  • Most Descriptive Compounds (MDC) [4]
  • Most Dissimilar Compounds (DIS) [5]

• Statistical analyisis

  • R2, MSE, MAE, RMSE, BIAS, Sensitivity, Positive Predicted Values
  • Yates analysis
  • Receiver operating characteristic (ROC)
  • Precision-Recal
  • Matrix-Matrix Euclidean, Manhattan, Cosine and Mahalanobis distances

• Numerical analysis

  • Estimate of an integral over a xy region (numerical integration using the trapezoid rule)
  • Natural cubic spline interpolation and prediction
  • Ordinary Least-Squares (OrdinaryLeastSquares)
  • Linear Equation Solver (SolveLSE)
  • Singular value decomposition

• Optimization

  • Nelder-Mead simplex algorithm

Moreover for some algorithms is possible to run validation methods with parallel computing to be faster:

• Bootstrap k-fold Cross Validation (RGCV)
• Leave-One-Out
• Y-Scrambling [6]