sortedness 0.230501.9

Measures of projection quality

sortedness

sortedness is a measure of quality of data transformation, often dimensionality reduction. It is less sensitive to irrelevant distortions and return values in a more meaningful interval than Kruskal stress formula I.
This Python library / code provides a reference implementation for the functions presented here (paper unavailable until publication).

Overview

Local variants return a value for each provided point. The global variant returns a single value for all points. Any local variant can be used as a global measure by taking the mean value.

Local variants: sortedness(X, X_), pwsortedness(X, X_), rsortedness(X, X_).

Global variant: global_sortedness(X, X_).

Python installation

from package through pip

# Set up a virtualenv. 
python3 -m venv venv
source venv/bin/activate

# Install from PyPI
pip install -U sortedness

from source

git clone https://github.com/sortedness/sortedness
cd sortedness
poetry install

Examples

Sortedness

import numpy as np
from numpy.random import permutation
from sklearn.decomposition import PCA

from sortedness.local import sortedness

mean = (1, 2)
cov = np.eye(2)
rng = np.random.default_rng(seed=0)
original = rng.multivariate_normal(mean, cov, size=12)
projected2 = PCA(n_components=2).fit_transform(original)
projected1 = PCA(n_components=1).fit_transform(original)
np.random.seed(0)
projectedrnd = permutation(original)

s = sortedness(original, original)
print(min(s), max(s), s)
"""
1.0 1.0 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
"""

s = sortedness(original, projected2)
print(min(s), max(s), s)
"""
1.0 1.0 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
"""

s = sortedness(original, projected1)
print(min(s), max(s), s)
"""
0.432937128932 0.944810120534 [0.43293713 0.53333015 0.88412753 0.94481012 0.81485109 0.81330052
 0.76691474 0.91169619 0.88998817 0.90102615 0.61372341 0.86996213]
"""

s = sortedness(original, projectedrnd)

Pairwise sortedness

import numpy as np
from numpy.random import permutation
from sklearn.decomposition import PCA

from sortedness.local import pwsortedness

mean = (1, 2)
cov = np.eye(2)
rng = np.random.default_rng(seed=0)
original = rng.multivariate_normal(mean, cov, size=12)
projected2 = PCA(n_components=2).fit_transform(original)
projected1 = PCA(n_components=1).fit_transform(original)
np.random.seed(0)
projectedrnd = permutation(original)

s = pwsortedness(original, original)
print(min(s), max(s), s)
"""
1.0 1.0 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
"""

s = pwsortedness(original, projected2)
print(min(s), max(s), s)
"""
1.0 1.0 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
"""

s = pwsortedness(original, projected1)
print(min(s), max(s), s)
"""
0.730078995423 0.837310352695 [0.75892647 0.730079   0.83496865 0.73161226 0.75376525 0.83301104
 0.76695755 0.74759156 0.81434161 0.74067221 0.74425225 0.83731035]
"""

s = pwsortedness(original, projectedrnd)

print(min(s), max(s), s)

"""
-0.198780473657 0.147224384381 [-0.19878047 -0.14125391  0.03276727 -0.092844   -0.0866695   0.14722438
 -0.07603536 -0.08916877 -0.1373848  -0.10933483 -0.07774488  0.05404383]
"""

** Copyright (c) 2022. Davi Pereira dos Santos and Tacito Neves**

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