sortedness 0.230501.10

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 import sortedness

# Some synthetic data.
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)

# Print `min`, `mean`, and `max` values.
s = sortedness(original, original)
print(min(s), sum(s) / len(s), max(s))
"""
1.0 1.0 1.0
"""

s = sortedness(original, projected2)
print(min(s), sum(s) / len(s), max(s))
"""
1.0 1.0 1.0
"""

s = sortedness(original, projected1)
print(min(s), sum(s) / len(s), max(s))
"""
0.432937128932 0.7813889452999166 0.944810120534
"""

s = sortedness(original, projectedrnd)
print(min(s), sum(s) / len(s), max(s))
"""
-0.578096068617 -0.06328160775358334 0.396112816715
"""

Pairwise sortedness

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

from sortedness import pwsortedness

# Some synthetic data.
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)

# Print `min`, `mean`, and `max` values.
s = pwsortedness(original, original)
print(min(s), sum(s) / len(s), max(s))
"""
1.0 1.0 1.0
"""

s = pwsortedness(original, projected2)
print(min(s), sum(s) / len(s), max(s))
"""
1.0 1.0 1.0
"""

s = pwsortedness(original, projected1)
print(min(s), sum(s) / len(s), max(s))
"""
0.730078995423 0.7744573488776667 0.837310352695
"""

s = pwsortedness(original, projectedrnd)
print(min(s), sum(s) / len(s), max(s))
"""
-0.198780473657 -0.0645984203715 0.147224384381
"""

Sortedness

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

from sortedness import global_pwsortedness

# Some synthetic data.
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)

# Print measurement result and p-value.
s = global_pwsortedness(original, original)
print(list(s))
"""
[1.0, 3.6741408919675163e-93]
"""

s = global_pwsortedness(original, projected2)
print(list(s))
"""
[1.0, 3.6741408919675163e-93]
"""

s = global_pwsortedness(original, projected1)
print(list(s))
"""
[0.7715617715617715, 5.240847664048334e-20]
"""

s = global_pwsortedness(original, projectedrnd)
print(list(s))
"""
[-0.06107226107226107, 0.46847188611226276]
"""

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

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