Module sortedness.trustworthiness

Expand source code 
#  Copyright (c) 2023. Davi Pereira dos Santos
#  This file is part of the sortedness project.
#  Please respect the license - more about this in the section (*) below.
#
#  sortedness is free software: you can redistribute it and/or modify
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#  part of this work is illegal and it is unethical regarding the effort and
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from math import nan

import numpy as np
from numpy import eye, where, setdiff1d
from numpy.random import shuffle
from sklearn.decomposition import PCA

from sortedness.rank import rank_by_distances


def continuity(X, X_, k=5, return_pvalues=False):
    """
    'continuity' of each point separately.

    >>> import numpy as np
    >>> from functools import partial
    >>> from scipy.stats import spearmanr, weightedtau
    >>> mean = (1, 2)
    >>> cov = eye(2)
    >>> rng = np.random.default_rng(seed=0)
    >>> original = rng.multivariate_normal(mean, cov, size=12)
    >>> s = continuity(original, original)
    >>> min(s), max(s), s
    (1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
    >>> projected = PCA(n_components=2).fit_transform(original)
    >>> s = continuity(original, projected)
    >>> min(s), max(s), s
    (1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
    >>> projected = PCA(n_components=1).fit_transform(original)
    >>> s, pvalues = continuity(original, projected, return_pvalues=True)
    >>> min(s), max(s), s
    (0.8, 1.0, array([0.95, 0.8 , 0.95, 1.  , 0.9 , 0.95, 0.95, 1.  , 0.95, 1.  , 0.85,
           0.9 ]))
    >>> pvalues
    array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan])


    Parameters
    ----------
    k
    X
        matrix with an instance by row in a given space (often the original one)
    X_
        matrix with an instance by row in another given space (often the projected one)
    return_pvalues
        Add dummy p-values to result (NaNs)

    Returns
    -------
    List of values, one for each instance

    """
    return trustworthiness(X_, X, k, return_pvalues)


def trustworthiness(X, X_, k=5, return_pvalues=False):
    """
    'trustworthiness' of each point separately.

    >>> import numpy as np
    >>> from functools import partial
    >>> from scipy.stats import spearmanr, weightedtau
    >>> mean = (1, 2)
    >>> cov = eye(2)
    >>> rng = np.random.default_rng(seed=0)
    >>> original = rng.multivariate_normal(mean, cov, size=12)
    >>> s = trustworthiness(original, original)
    >>> min(s), max(s), s
    (1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
    >>> projected = PCA(n_components=2).fit_transform(original)
    >>> s = trustworthiness(original, projected)
    >>> min(s), max(s), s
    (1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
    >>> projected = PCA(n_components=1).fit_transform(original)
    >>> s, pvalues = trustworthiness(original, projected, return_pvalues=True)
    >>> min(s), max(s), s
    (0.75, 1.0, array([0.8 , 0.75, 0.9 , 1.  , 0.85, 0.9 , 0.95, 1.  , 0.95, 1.  , 0.85,
           0.8 ]))
    >>> pvalues
    array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan])


    Parameters
    ----------
    k
    X
        matrix with an instance by row in a given space (often the original one)
    X_
        matrix with an instance by row in another given space (often the projected one)
    return_pvalues
        Add dummy p-values to result (NaNs)

    Returns
    -------
    List of values, one for each instance

    """
    result, pvalues = [], []
    n = len(X)
    for a, b in zip(X, X_):
        ra = rank_by_distances(X, a, "min")
        rb = rank_by_distances(X_, b, "min")
        a_neighbors = where(ra <= k)
        b_neighbors = where(rb <= k)
        U = setdiff1d(b_neighbors, a_neighbors)
        r = 1 - 2 * sum(ra[U] - k) / k / (2 * n - 3 * k - 1)
        result.append(r)
    result = np.array(result)
    if return_pvalues:
        return result, np.array([nan for _ in result])
    return result

Functions

def continuity(X, X_, k=5, return_pvalues=False)

'continuity' of each point separately.

>>> import numpy as np
>>> from functools import partial
>>> from scipy.stats import spearmanr, weightedtau
>>> mean = (1, 2)
>>> cov = eye(2)
>>> rng = np.random.default_rng(seed=0)
>>> original = rng.multivariate_normal(mean, cov, size=12)
>>> s = continuity(original, original)
>>> min(s), max(s), s
(1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
>>> projected = PCA(n_components=2).fit_transform(original)
>>> s = continuity(original, projected)
>>> min(s), max(s), s
(1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
>>> projected = PCA(n_components=1).fit_transform(original)
>>> s, pvalues = continuity(original, projected, return_pvalues=True)
>>> min(s), max(s), s
(0.8, 1.0, array([0.95, 0.8 , 0.95, 1.  , 0.9 , 0.95, 0.95, 1.  , 0.95, 1.  , 0.85,
       0.9 ]))
>>> pvalues
array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan])

Parameters

k
 
X
matrix with an instance by row in a given space (often the original one)
X_
matrix with an instance by row in another given space (often the projected one)
return_pvalues
Add dummy p-values to result (NaNs)

Returns

List of values, one for each instance
 
Expand source code 
def continuity(X, X_, k=5, return_pvalues=False):
    """
    'continuity' of each point separately.

    >>> import numpy as np
    >>> from functools import partial
    >>> from scipy.stats import spearmanr, weightedtau
    >>> mean = (1, 2)
    >>> cov = eye(2)
    >>> rng = np.random.default_rng(seed=0)
    >>> original = rng.multivariate_normal(mean, cov, size=12)
    >>> s = continuity(original, original)
    >>> min(s), max(s), s
    (1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
    >>> projected = PCA(n_components=2).fit_transform(original)
    >>> s = continuity(original, projected)
    >>> min(s), max(s), s
    (1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
    >>> projected = PCA(n_components=1).fit_transform(original)
    >>> s, pvalues = continuity(original, projected, return_pvalues=True)
    >>> min(s), max(s), s
    (0.8, 1.0, array([0.95, 0.8 , 0.95, 1.  , 0.9 , 0.95, 0.95, 1.  , 0.95, 1.  , 0.85,
           0.9 ]))
    >>> pvalues
    array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan])


    Parameters
    ----------
    k
    X
        matrix with an instance by row in a given space (often the original one)
    X_
        matrix with an instance by row in another given space (often the projected one)
    return_pvalues
        Add dummy p-values to result (NaNs)

    Returns
    -------
    List of values, one for each instance

    """
    return trustworthiness(X_, X, k, return_pvalues)
def shuffle(x)

Modify a sequence in-place by shuffling its contents.

This function only shuffles the array along the first axis of a multi-dimensional array. The order of sub-arrays is changed but their contents remains the same.

Note

New code should use the ~numpy.random.Generator.shuffle method of a ~numpy.random.Generator instance instead; please see the :ref:random-quick-start.

Parameters

x : ndarray or MutableSequence
The array, list or mutable sequence to be shuffled.

Returns

None
 

See Also

random.Generator.shuffle
which should be used for new code.

Examples

>>> arr = np.arange(10)
>>> np.random.shuffle(arr)
>>> arr
[1 7 5 2 9 4 3 6 0 8] # random

Multi-dimensional arrays are only shuffled along the first axis:

>>> arr = np.arange(9).reshape((3, 3))
>>> np.random.shuffle(arr)
>>> arr
array([[3, 4, 5], # random
       [6, 7, 8],
       [0, 1, 2]])
def trustworthiness(X, X_, k=5, return_pvalues=False)

'trustworthiness' of each point separately.

>>> import numpy as np
>>> from functools import partial
>>> from scipy.stats import spearmanr, weightedtau
>>> mean = (1, 2)
>>> cov = eye(2)
>>> rng = np.random.default_rng(seed=0)
>>> original = rng.multivariate_normal(mean, cov, size=12)
>>> s = trustworthiness(original, original)
>>> min(s), max(s), s
(1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
>>> projected = PCA(n_components=2).fit_transform(original)
>>> s = trustworthiness(original, projected)
>>> min(s), max(s), s
(1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
>>> projected = PCA(n_components=1).fit_transform(original)
>>> s, pvalues = trustworthiness(original, projected, return_pvalues=True)
>>> min(s), max(s), s
(0.75, 1.0, array([0.8 , 0.75, 0.9 , 1.  , 0.85, 0.9 , 0.95, 1.  , 0.95, 1.  , 0.85,
       0.8 ]))
>>> pvalues
array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan])

Parameters

k
 
X
matrix with an instance by row in a given space (often the original one)
X_
matrix with an instance by row in another given space (often the projected one)
return_pvalues
Add dummy p-values to result (NaNs)

Returns

List of values, one for each instance
 
Expand source code 
def trustworthiness(X, X_, k=5, return_pvalues=False):
    """
    'trustworthiness' of each point separately.

    >>> import numpy as np
    >>> from functools import partial
    >>> from scipy.stats import spearmanr, weightedtau
    >>> mean = (1, 2)
    >>> cov = eye(2)
    >>> rng = np.random.default_rng(seed=0)
    >>> original = rng.multivariate_normal(mean, cov, size=12)
    >>> s = trustworthiness(original, original)
    >>> min(s), max(s), s
    (1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
    >>> projected = PCA(n_components=2).fit_transform(original)
    >>> s = trustworthiness(original, projected)
    >>> min(s), max(s), s
    (1.0, 1.0, array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]))
    >>> projected = PCA(n_components=1).fit_transform(original)
    >>> s, pvalues = trustworthiness(original, projected, return_pvalues=True)
    >>> min(s), max(s), s
    (0.75, 1.0, array([0.8 , 0.75, 0.9 , 1.  , 0.85, 0.9 , 0.95, 1.  , 0.95, 1.  , 0.85,
           0.8 ]))
    >>> pvalues
    array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan])


    Parameters
    ----------
    k
    X
        matrix with an instance by row in a given space (often the original one)
    X_
        matrix with an instance by row in another given space (often the projected one)
    return_pvalues
        Add dummy p-values to result (NaNs)

    Returns
    -------
    List of values, one for each instance

    """
    result, pvalues = [], []
    n = len(X)
    for a, b in zip(X, X_):
        ra = rank_by_distances(X, a, "min")
        rb = rank_by_distances(X_, b, "min")
        a_neighbors = where(ra <= k)
        b_neighbors = where(rb <= k)
        U = setdiff1d(b_neighbors, a_neighbors)
        r = 1 - 2 * sum(ra[U] - k) / k / (2 * n - 3 * k - 1)
        result.append(r)
    result = np.array(result)
    if return_pvalues:
        return result, np.array([nan for _ in result])
    return result