Laplacian Singular Values

DOI

10.2991/asum.k.210827.019How to use a DOI?

Keywords

Singular value decomposition, Dimensionality reduction, Weighted graph, Generalized eigenvalue problem, Data processing

Abstract

In this contribution, we focus on extending the Laplacian processing used in data-driven dimensionality reduction based on weighted graphs by incorporating the concept of singular value decomposition. We indicate a novel point of view on generalized eigenvalue problem by pointing out geometric meaning of factorization matrices. We demonstrate that classical eigenvalue problem of normalized Laplacian, generalized eigenvalue problem of pure Laplacian and singular value decomposition of specific altered Laplacian form are mutually equivalent problems and discuss some of its theoretical implications.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Jiří Janeček
AU  - Irina Perfilieva
PY  - 2021
DA  - 2021/08/30
TI  - Laplacian Singular Values
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 142
EP  - 146
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.019
DO  - 10.2991/asum.k.210827.019
ID  - Janeček2021
ER  -