References & Citations
Mathematics > Numerical Analysis
Title: Higher order multi-dimension reduction methods via Einstein-product
(Submitted on 27 Mar 2024 (v1), last revised 30 Mar 2024 (this version, v2))
Abstract: This paper explores the extension of dimension reduction (DR) techniques to the multi-dimension case by using the Einstein product. Our focus lies on graph-based methods, encompassing both linear and nonlinear approaches, within both supervised and unsupervised learning paradigms. Additionally, we investigate variants such as repulsion graphs and kernel methods for linear approaches. Furthermore, we present two generalizations for each method, based on single or multiple weights. We demonstrate the straightforward nature of these generalizations and provide theoretical insights. Numerical experiments are conducted, and results are compared with original methods, highlighting the efficiency of our proposed methods, particularly in handling high-dimensional data such as color images.
Submission history
From: Alaeddine Zahir [view email][v1] Wed, 27 Mar 2024 00:55:16 GMT (349kb,D)
[v2] Sat, 30 Mar 2024 00:13:21 GMT (345kb,D)
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