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