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Singular Value Decomposition

In: Mathematical Introduction to Data Science

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  • Sven A. Wegner

Abstract

We first present an approach to singular value decomposition (SVD) for non-square matrices based only on standard methods of linear algebra. Using the Courant-Fischer formula, we then link SVD to the greedy algorithm already discussed in Chapter 6 . This is followed by several applications such as dimensionality reduction of datasets and lower-rank approximation of matrices. As a concrete example, we discuss image compression. Finally, we illustrate the technique of principal component analysis (PCA), as well as the method of collaborative filtering in the context of movie ratings.

Suggested Citation

  • Sven A. Wegner, 2024. "Singular Value Decomposition," Springer Books, in: Mathematical Introduction to Data Science, chapter 0, pages 89-114, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-69426-8_7
    DOI: 10.1007/978-3-662-69426-8_7
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