PCA: Unveiling the Structure of High-Dimensional Data
Principal Component Analysis (PCA) is a foundational technique in data analysis, used for dimensionality reduction while preserving as much variance as possible. This guide delves into the mathematical formulation of PCA, discusses the limitations of direct covariance matrix computation, and explains the Gram matrix approach as a practical alternative. Overview of Principal Component Analysis (PCA) PCA is a technique used to transform data into a set of orthogonal components that capture the maximum variance in the data. These components, known as principal components, help simplify complex datasets by reducing their dimensions while retaining key information. PCA is widely used in data preprocessing, visualization, and feature extraction. Mathematical Formulation Step 1: Center the Data 1. Centering : To apply PCA, start by centering the data. This involves subtracting the mean of each fea...
