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PCA (Principal Component Analysis) in Python - ML From Scratch 11

Implement a PCA algorithm using only built-in Python modules and numpy, and learn about the math behind this popular ML algorithm.


In this Machine Learning from Scratch Tutorial, we are going to implement a PCA algorithm using only built-in Python modules and numpy. We will also learn about the concept and the math behind this popular ML algorithm.

All algorithms from this course can be found on GitHub together with example tests.

Implementation

import numpy as np

class PCA:

    def __init__(self, n_components):
        self.n_components = n_components
        self.components = None
        self.mean = None

    def fit(self, X):
        # Mean centering
        self.mean = np.mean(X, axis=0)
        X = X - self.mean
        # covariance, function needs samples as columns
        cov = np.cov(X.T)
        # eigenvalues, eigenvectors
        eigenvalues, eigenvectors = np.linalg.eig(cov)
        # -> eigenvector v = [:,i] column vector, transpose for easier calculations
        # sort eigenvectors
        eigenvectors = eigenvectors.T
        idxs = np.argsort(eigenvalues)[::-1]
        eigenvalues = eigenvalues[idxs]
        eigenvectors = eigenvectors[idxs]
        # store first n eigenvectors
        self.components = eigenvectors[0:self.n_components]

    def transform(self, X):
        # project data
        X = X - self.mean
        return np.dot(X, self.components.T)

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