plot_affinity.py

"""
=================
Affine invariance
=================

.. currentmodule:: fastcan

In this examples, we will compare the robustness of the three feature
selection methods on affine transformed features.
"""

# Authors: The fastcan developers
# SPDX-License-Identifier: MIT

# %%
# Initialize test
# ---------------
# The three feature selection methods, i.e., OMP, OLS, and :class:`FastCan`,
# will select three features from the 10 features of `diabetes` dataset. It can be
# seen, the three methods select the same features.

import numpy as np
from sklearn.datasets import load_diabetes
from sklearn.linear_model import OrthogonalMatchingPursuit

from fastcan import FastCan
from fastcan.utils import ols

X, y = load_diabetes(return_X_y=True)

n_selected = 3
omp_selector = OrthogonalMatchingPursuit(n_nonzero_coefs=n_selected)
fastcan_selector = FastCan(n_features_to_select=n_selected, verbose=0)
(ids_omp,) = omp_selector.fit(X, y).coef_.nonzero()
ids_ols, _ = ols(X, y, n_selected)
ids_fastcan = fastcan_selector.fit(X, y).indices_

print("Indices of features selected by:")
print("OMP: ", np.sort(ids_omp))
print("OLS: ", np.sort(ids_ols))
print("FastCan: ", np.sort(ids_fastcan))


# %%
# Affine transformation
# ---------------------
# In this test, the 10 features of ``diabetes`` dataset will be randomly polluted
# by the affine transformation. The three feature selection methods will select
# three features from the polluted features. The more stable the result, the better.


n_features = X.shape[1]
rng = np.random.default_rng()

ids_omp_all = []
ids_ols_all = []
ids_fastcan_all = []
for i in range(10):
    X_affine = X @ np.diag(rng.random(n_features)) + rng.random(n_features)

    (ids_omp,) = omp_selector.fit(X_affine, y).coef_.nonzero()
    ids_ols, _ = ols(X_affine, y, n_selected)
    ids_fastcan = fastcan_selector.fit(X_affine, y).indices_
    ids_omp_all += ids_omp.tolist()
    ids_ols_all += ids_ols.tolist()
    ids_fastcan_all += ids_fastcan.tolist()

# %%
# Plot results
# ------------
# It can be seen, only :class:`FastCan` has robust results when the feature
# is polluted by the affine transformation.

import matplotlib.pyplot as plt

bin_lims = np.arange(n_features + 1)
counts_omp, _ = np.histogram(ids_omp_all, bins=bin_lims)
counts_ols, _ = np.histogram(ids_ols_all, bins=bin_lims)
counts_fastcan, _ = np.histogram(ids_fastcan_all, bins=bin_lims)

fig, axs = plt.subplots(1, 3, figsize=(8, 3))

axs[0].bar(bin_lims[:-1], counts_omp)
axs[0].set_xticks(bin_lims[:-1])
axs[0].set_ylim((0, 11))
axs[0].set_title("OMP")
axs[0].set_xlabel("Feature Index")
axs[0].set_ylabel("Count of Selected Times")


axs[1].bar(bin_lims[:-1], counts_ols)
axs[1].set_xticks(bin_lims[:-1])
axs[1].set_ylim((0, 11))
axs[1].set_title("OLS")
axs[1].set_xlabel("Feature Index")

axs[2].bar(bin_lims[:-1], counts_fastcan)
axs[2].set_xticks(bin_lims[:-1])
axs[2].set_ylim((0, 11))
axs[2].set_title("FastCan")
axs[2].set_xlabel("Feature Index")

plt.tight_layout()
plt.show()