machine_learning.dimensionality_reduction

Requirements:

  • numpy version 1.21

  • scipy version 1.3.3

Notes:

  • Each column of the features matrix corresponds to a class item

Functions

column_reshape(→ numpy.ndarray)

Function to reshape a row Numpy array into a column Numpy array

covariance_between_classes(→ numpy.ndarray)

Function to compute the covariance matrix between multiple classes

covariance_within_classes(→ numpy.ndarray)

Function to compute the covariance matrix inside each class.

linear_discriminant_analysis(→ numpy.ndarray)

Linear Discriminant Analysis.

principal_component_analysis(→ numpy.ndarray)

Principal Component Analysis.

t_distributed_stochastic_neighbor_embedding(...)

t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm for

test_linear_discriminant_analysis(→ None)

test_principal_component_analysis(→ None)

test_t_distributed_stochastic_neighbor_embedding(→ None)

Test t-SNE algorithm with various input conditions.

Module Contents

machine_learning.dimensionality_reduction.column_reshape(input_array: numpy.ndarray) → numpy.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]])

machine_learning.dimensionality_reduction.covariance_between_classes(features: numpy.ndarray, labels: numpy.ndarray, classes: int) → numpy.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. ]])

machine_learning.dimensionality_reduction.covariance_within_classes(features: numpy.ndarray, labels: numpy.ndarray, classes: int) → numpy.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]])

machine_learning.dimensionality_reduction.linear_discriminant_analysis(features: numpy.ndarray, labels: numpy.ndarray, classes: int, dimensions: int) → numpy.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()
machine_learning.dimensionality_reduction.principal_component_analysis(features: numpy.ndarray, dimensions: int) → numpy.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()
machine_learning.dimensionality_reduction.t_distributed_stochastic_neighbor_embedding(features: numpy.ndarray, dimensions: int = 2, perplexity: float = 30.0, learning_rate: float = 200.0, max_iterations: int = 1000, random_state: int = 42) → numpy.ndarray

t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm for dimensionality reduction.

t-SNE is a machine learning algorithm for visualization developed by Laurens van der Maaten and Geoffrey Hinton. It is a nonlinear dimensionality reduction technique particularly well suited for the visualization of high-dimensional datasets.

For more details, see: https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding Original paper: https://www.jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf

Parameters:

  • features: Input data matrix where each column represents a data point

  • dimensions: Number of dimensions for the output (typically 2 or 3)

  • perplexity: Controls the effective number of neighbors (typically 5-50)

  • learning_rate: Learning rate for gradient descent

  • max_iterations: Maximum number of optimization iterations

  • random_state: Random seed for reproducible results

Returns:

  • projected_data: Low-dimensional representation of the input data

>>> # Test with simple 3D to 2D reduction
>>> features = np.array([[1, 2], [3, 4], [5, 6], [7, 8]], dtype=float).T
>>> result = t_distributed_stochastic_neighbor_embedding(
...     features, dimensions=2, max_iterations=10
... )
>>> result.shape
(2, 4)

>>> # Test with invalid dimensions
>>> try:
...     t_distributed_stochastic_neighbor_embedding(features, dimensions=0)
... except ValueError as e:
...     print("ValueError raised for invalid dimensions")
ValueError raised for invalid dimensions
machine_learning.dimensionality_reduction.test_linear_discriminant_analysis() → None
machine_learning.dimensionality_reduction.test_principal_component_analysis() → None
machine_learning.dimensionality_reduction.test_t_distributed_stochastic_neighbor_embedding() → None

Test t-SNE algorithm with various input conditions.