Feature Extraction Using Principal Component Analysis

This article provides an in-depth exploration of Principal Component Analysis (PCA) as a feature extraction method for pattern recognition, along with MATLAB implementation details. PCA is a widely-used statistical technique that reduces high-dimensional data to more manageable low-dimensional spaces. The algorithm calculates the covariance matrix of the dataset and identifies eigenvectors with maximum variance, which form the basis for constructing a new low-dimensional feature space. We present fundamental mathematical formulations and MATLAB code examples to demonstrate practical implementation, including the use of built-in functions like cov() for covariance computation and eig() for eigenvalue decomposition. The implementation covers data standardization, eigenvector selection based on variance thresholds, and projection of original data onto principal components. These code examples will help readers understand both the theoretical foundations and practical application of PCA algorithms in dimensionality reduction tasks.