mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 15:01:08 +00:00
3f094fe49d
* Python linting: Add ruff rules for Pandas-vet and Pytest-style
* updating DIRECTORY.md
---------
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
199 lines
7.0 KiB
Python
199 lines
7.0 KiB
Python
# Copyright (c) 2023 Diego Gasco (diego.gasco99@gmail.com), Diegomangasco on GitHub
|
|
|
|
"""
|
|
Requirements:
|
|
- numpy version 1.21
|
|
- scipy version 1.3.3
|
|
Notes:
|
|
- Each column of the features matrix corresponds to a class item
|
|
"""
|
|
|
|
import logging
|
|
|
|
import numpy as np
|
|
import pytest
|
|
from scipy.linalg import eigh
|
|
|
|
logging.basicConfig(level=logging.INFO, format="%(message)s")
|
|
|
|
|
|
def column_reshape(input_array: np.ndarray) -> np.ndarray:
|
|
"""Function to reshape a row Numpy array into a column Numpy array
|
|
>>> input_array = np.array([1, 2, 3])
|
|
>>> column_reshape(input_array)
|
|
array([[1],
|
|
[2],
|
|
[3]])
|
|
"""
|
|
|
|
return input_array.reshape((input_array.size, 1))
|
|
|
|
|
|
def covariance_within_classes(
|
|
features: np.ndarray, labels: np.ndarray, classes: int
|
|
) -> np.ndarray:
|
|
"""Function to compute the covariance matrix inside each class.
|
|
>>> features = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
|
|
>>> labels = np.array([0, 1, 0])
|
|
>>> covariance_within_classes(features, labels, 2)
|
|
array([[0.66666667, 0.66666667, 0.66666667],
|
|
[0.66666667, 0.66666667, 0.66666667],
|
|
[0.66666667, 0.66666667, 0.66666667]])
|
|
"""
|
|
|
|
covariance_sum = np.nan
|
|
for i in range(classes):
|
|
data = features[:, labels == i]
|
|
data_mean = data.mean(1)
|
|
# Centralize the data of class i
|
|
centered_data = data - column_reshape(data_mean)
|
|
if i > 0:
|
|
# If covariance_sum is not None
|
|
covariance_sum += np.dot(centered_data, centered_data.T)
|
|
else:
|
|
# If covariance_sum is np.nan (i.e. first loop)
|
|
covariance_sum = np.dot(centered_data, centered_data.T)
|
|
|
|
return covariance_sum / features.shape[1]
|
|
|
|
|
|
def covariance_between_classes(
|
|
features: np.ndarray, labels: np.ndarray, classes: int
|
|
) -> np.ndarray:
|
|
"""Function to compute the covariance matrix between multiple classes
|
|
>>> features = np.array([[9, 2, 3], [4, 3, 6], [1, 8, 9]])
|
|
>>> labels = np.array([0, 1, 0])
|
|
>>> covariance_between_classes(features, labels, 2)
|
|
array([[ 3.55555556, 1.77777778, -2.66666667],
|
|
[ 1.77777778, 0.88888889, -1.33333333],
|
|
[-2.66666667, -1.33333333, 2. ]])
|
|
"""
|
|
|
|
general_data_mean = features.mean(1)
|
|
covariance_sum = np.nan
|
|
for i in range(classes):
|
|
data = features[:, labels == i]
|
|
device_data = data.shape[1]
|
|
data_mean = data.mean(1)
|
|
if i > 0:
|
|
# If covariance_sum is not None
|
|
covariance_sum += device_data * np.dot(
|
|
column_reshape(data_mean) - column_reshape(general_data_mean),
|
|
(column_reshape(data_mean) - column_reshape(general_data_mean)).T,
|
|
)
|
|
else:
|
|
# If covariance_sum is np.nan (i.e. first loop)
|
|
covariance_sum = device_data * np.dot(
|
|
column_reshape(data_mean) - column_reshape(general_data_mean),
|
|
(column_reshape(data_mean) - column_reshape(general_data_mean)).T,
|
|
)
|
|
|
|
return covariance_sum / features.shape[1]
|
|
|
|
|
|
def principal_component_analysis(features: np.ndarray, dimensions: int) -> np.ndarray:
|
|
"""
|
|
Principal Component Analysis.
|
|
|
|
For more details, see: https://en.wikipedia.org/wiki/Principal_component_analysis.
|
|
Parameters:
|
|
* features: the features extracted from the dataset
|
|
* dimensions: to filter the projected data for the desired dimension
|
|
|
|
>>> test_principal_component_analysis()
|
|
"""
|
|
|
|
# Check if the features have been loaded
|
|
if features.any():
|
|
data_mean = features.mean(1)
|
|
# Center the dataset
|
|
centered_data = features - np.reshape(data_mean, (data_mean.size, 1))
|
|
covariance_matrix = np.dot(centered_data, centered_data.T) / features.shape[1]
|
|
_, eigenvectors = np.linalg.eigh(covariance_matrix)
|
|
# Take all the columns in the reverse order (-1), and then takes only the first
|
|
filtered_eigenvectors = eigenvectors[:, ::-1][:, 0:dimensions]
|
|
# Project the database on the new space
|
|
projected_data = np.dot(filtered_eigenvectors.T, features)
|
|
logging.info("Principal Component Analysis computed")
|
|
|
|
return projected_data
|
|
else:
|
|
logging.basicConfig(level=logging.ERROR, format="%(message)s", force=True)
|
|
logging.error("Dataset empty")
|
|
raise AssertionError
|
|
|
|
|
|
def linear_discriminant_analysis(
|
|
features: np.ndarray, labels: np.ndarray, classes: int, dimensions: int
|
|
) -> np.ndarray:
|
|
"""
|
|
Linear Discriminant Analysis.
|
|
|
|
For more details, see: https://en.wikipedia.org/wiki/Linear_discriminant_analysis.
|
|
Parameters:
|
|
* features: the features extracted from the dataset
|
|
* labels: the class labels of the features
|
|
* classes: the number of classes present in the dataset
|
|
* dimensions: to filter the projected data for the desired dimension
|
|
|
|
>>> test_linear_discriminant_analysis()
|
|
"""
|
|
|
|
# Check if the dimension desired is less than the number of classes
|
|
assert classes > dimensions
|
|
|
|
# Check if features have been already loaded
|
|
if features.any:
|
|
_, eigenvectors = eigh(
|
|
covariance_between_classes(features, labels, classes),
|
|
covariance_within_classes(features, labels, classes),
|
|
)
|
|
filtered_eigenvectors = eigenvectors[:, ::-1][:, :dimensions]
|
|
svd_matrix, _, _ = np.linalg.svd(filtered_eigenvectors)
|
|
filtered_svd_matrix = svd_matrix[:, 0:dimensions]
|
|
projected_data = np.dot(filtered_svd_matrix.T, features)
|
|
logging.info("Linear Discriminant Analysis computed")
|
|
|
|
return projected_data
|
|
else:
|
|
logging.basicConfig(level=logging.ERROR, format="%(message)s", force=True)
|
|
logging.error("Dataset empty")
|
|
raise AssertionError
|
|
|
|
|
|
def test_linear_discriminant_analysis() -> None:
|
|
# Create dummy dataset with 2 classes and 3 features
|
|
features = np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]])
|
|
labels = np.array([0, 0, 0, 1, 1])
|
|
classes = 2
|
|
dimensions = 2
|
|
|
|
# Assert that the function raises an AssertionError if dimensions > classes
|
|
with pytest.raises(AssertionError) as error_info: # noqa: PT012
|
|
projected_data = linear_discriminant_analysis(
|
|
features, labels, classes, dimensions
|
|
)
|
|
if isinstance(projected_data, np.ndarray):
|
|
raise AssertionError(
|
|
"Did not raise AssertionError for dimensions > classes"
|
|
)
|
|
assert error_info.type is AssertionError
|
|
|
|
|
|
def test_principal_component_analysis() -> None:
|
|
features = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
|
|
dimensions = 2
|
|
expected_output = np.array([[6.92820323, 8.66025404, 10.39230485], [3.0, 3.0, 3.0]])
|
|
|
|
with pytest.raises(AssertionError) as error_info: # noqa: PT012
|
|
output = principal_component_analysis(features, dimensions)
|
|
if not np.allclose(expected_output, output):
|
|
raise AssertionError
|
|
assert error_info.type is AssertionError
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|