Year: 2023
Type: preprint
Abstract: The goal of this paper is to revisit Kernel Principal Component Analysis (KPCA) through dualization of a difference of convex functions. This allows to naturally extend KPCA to multiple objective functions and leads to efficient gradient-based algorithms avoiding the expensive SVD of the Gram matrix. Particularly, we consider objective functions that can be written as Moreau envelopes, demonstrating how to promote robustness and sparsity within the same framework. The proposed method is evaluated on synthetic and real-world benchmarks, showing significant speedup in KPCA training time as well as highlighting the benefits in terms of robustness and sparsity.
Source: arXiv (Cornell University)
Authors: Tonin, Francesco, Lambert, Alex, Patrinos, Panagiotis, Suykens, Johan A. K.
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G160199020, Structured Low-Rank matrix / tensor approximation: numerical optimization-based algorithms and applications, A unifying algorithmic framework for structured optimization, Linking redox and hormonal signalling in Arabidopsis plants with altered levels of a stress-inducible glycosyltransferase, Learning to optimize nonconvex problems: provably and efficiently, G4829754272, G495187929, Deep Restricted Kernel Machines: Methods and Foundations, G6057626455, G6182351167, G6221759109, Risk-averse Control and Dynamic Optimization: Bridging the Gap Between Robust and Stochastic Control, G675632898, G7564167306, G8017291778, G8829997307
OpenAlex ID: W4380353923