Singular Value Decomposition And Principal Component Analysis: A Practical Introduction For Data Analysis
Keywords:
Singular Value Decomposition (SVD), Principal Component Analysis (PCA), Dimensionality Reduction, Eigenvalues, Eigenvectors, Data Analysis, Covariance MatrixAbstract
Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) are foundational techniques in modern data analysis, widely used for dimensionality reduction, feature extraction, and data visualization. This paper offers a comprehensive yet accessible introduction to the mathematical foundations, computational strategies, and practical applications of SVD and PCA. Detailed attention is given to their algebraic properties, use in handling large data matrices, and their implementation. The study provides an up-to-date review of literature and underscoring the ongoing relevance of these techniques in fields such as image processing, genetics, finance, and machine learning. The discussion also covers alternative methods for dimensionality reduction and highlights best practices for determining the number of principal components. This work aims to serve as both a tutorial and a reference for researchers and practitioners.
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