Principal Component Analysis and Canonical Correlation Analysis: Implementation and Case Studies

This article demonstrates how to perform case studies using Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA). PCA is a dimensionality reduction technique that extracts key features from datasets to reduce complexity, typically implemented through eigenvalue decomposition of the covariance matrix or SVD operations. Canonical Correlation Analysis is a statistical method for examining relationships between two sets of variables, often computed using covariance matrices and linear combinations. By integrating both techniques, we can gain deeper insights into datasets and extract meaningful information for improved decision-making. Through practical examples, this article illustrates data analysis applications using these methods, with detailed explanations of the analysis process. We provide guidance on interpreting results, including how to assess principal component contributions in PCA and measure correlation significance in CCA, enabling readers to better understand their practical implications and implementation strategies.