Added Principal Component Analysis

machine_learning/principal_component_analysis.py

@@ -0,0 +1,102 @@
+"""
+Principal Component Analysis (PCA) is an unsupervised learning
+algorithm that is used for the dimensionality reduction in machine
+learning. It  is a statistical procedure that uses an orthogonal
+transformation to convert a set of observations of possibly correlated
+variables into a set of values of linearly uncorrelated variables called
+principal components.
+
+Data: The data used for PCA is a set of 500 data points, each with 4
+features. The data is assumed to be in normal form.
+
+Reference: https://en.wikipedia.org/wiki/Principal_component_analysis
+
+"""
+
+import numpy as np
+
+
+class PCA:
+    def __init__(self, n_components: int) -> None:
+        """
+        Parameters:
+        n_components: The number of components required after dimensionality reduction
+
+        Create a PCA object with the given number of components
+        """
+        self.n = n_components
+        self.mean = None
+        self.components = None
+
+    def fit(self, vector: np.ndarray[float]) -> None:
+        """
+        Parameters:
+        vector: The data to be fitted
+
+        Fit the PCA model to the given data
+        The process of performing PCA involves the following steps:
+        1. Normalize the data by subtracting the mean from each data point
+        2. Calculate the covariance matrix of the normalized data
+        3. Calculate the eigenvalues and eigenvectors of the covariance matrix
+        4. Sort the eigenvalues and eigenvectors in descending order of the eigenvalues
+        5. Choose the first n eigenvectors, where n is the number of components
+
+        >>> test_data = np.array([
+        ... [1.2, 2.3, 3.4], [4.5, 5.6, 6.7], [7.8, 8.9, 9.0], [10.1, 11.2, 12.3]
+        ... ])
+        >>> test_pca = PCA(2)
+        >>> test_pca.fit(test_data)
+        """
+        self.mean = np.mean(vector, axis=0)
+        vector = vector - self.mean
+
+        cov = np.cov(vector.T)
+
+        eigen_vector, eigen_value = np.linalg.eig(cov)
+        eigen_vector = eigen_vector.T
+
+        indexes = np.argsort(eigen_value)[::-1]
+        eigen_vector = eigen_vector[indexes]
+
+        self.components = eigen_vector[: self.n]
+
+    def transform(self, vector: np.ndarray[float]) -> np.ndarray[float]:
+        """
+        Parameters:
+        vector: The data to be transformed
+
+        Transform the given data using the fitted PCA model
+
+        >>> test_data = np.array([
+        ... [1.2, 2.3, 3.4], [4.5, 5.6, 6.7], [7.8, 8.9, 9.0], [10.1, 11.2, 12.3]
+        ... ])
+        >>> test_pca = PCA(2)
+        >>> test_pca.fit(test_data)
+        >>> test_pca.transform(test_data)
+        array([[-208.09344033, -208.13166667],
+               [ -61.95844033,  -61.99666667],
+               [  84.02365433,   84.13833333],
+               [ 186.02822633,  185.99      ]])
+        """
+        vector = vector - self.mean
+        return np.dot(vector, np.transpose(self.components))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    X1 = np.random.normal(0, 1, 500)
+    X2 = np.random.normal(0, 1, 500)
+    X3 = np.random.normal(0, 1, 500)
+    X4 = np.random.normal(0, 1, 500)
+
+    data = np.column_stack((X1, X2, X3, X4))
+
+    pca = PCA(2)
+    pca.fit(data)
+    post_pca_data = pca.transform(data)
+
+    print("Shape of X (Data Points) is: ", data.shape)
+    print("Shape of X after PCA is: ", post_pca_data.shape)