A Tutorial on Singular Value Decomposition with Applications on Image Compression and Dimensionality Reduction
Yousef M. Jaradat, Mohammad Z. Masoud, Ismael Jannoud, Ahmad A. Manasrah, Mohammad Ahmad Alia · 2021
This paper introduces singular value decomposition (SVD), a major matrix decomposition technique. SVD serves as the underlining computational engine of many other techniques such as principal component analysis (PCA), eigen decomposition, matrix decomposition, Cholesky decomposition and others. SVD is utilized in many applications such as data analysis and dimensionality reduction, image compression, Google's PageRank algorithm, Netflix's recommender system and many more. This paper overviews the mathematics behind SVD in a simple way. It also applies SVD technique in image compression and in dimensionality reduction as the underlining technique of the PCA and data analysis.