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Eigenvalue and Generalized Eigenvalue Problems: Tutorial

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arxiv 1903.11240 v3 pith:C55LCZBM submitted 2019-03-25 stat.ML cs.LG

Benyamin Ghojogh , Fakhri Karray , Mark Crowley This is my paper · ORCID
classification stat.MLcs.LG
keywords eigenvaluegeneralizedproblemsanalysiscomponentintroduceprincipalproblem
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This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also provide examples from machine learning, including principal component analysis, kernel supervised principal component analysis, and Fisher discriminant analysis, which result in eigenvalue and generalized eigenvalue problems. Finally, we introduce the solutions to both eigenvalue and generalized eigenvalue problems.

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