Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithms

Francesco Tonin; Alex Lambert; Panagiotis Patrinos; Johan Suykens

ICML 2023poster1 citations

Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithms

Francesco Tonin, Alex Lambert, Panagiotis Patrinos, Johan Suykens

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 realworld benchmarks, showing significant speedup in KPCA training time as well as highlighting the benefits in terms of robustness and sparsity.

BibTeX

@inproceedings{icml2023_extendingkernelp,
  title = {Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithms},
  author = {Francesco Tonin and Alex Lambert and Panagiotis Patrinos and Johan Suykens},
  booktitle = {ICML 2023},
  year = {2023}
}