English

A Generalization of Principal Component Analysis

Machine Learning 2019-11-19 v2 Signal Processing Machine Learning

Abstract

Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of principal components. We present a gradient ascent algorithm to solve the problem. For the kernel version of generalized PCA, we show that the solutions can be obtained as fixed points of a simple single-layer recurrent neural network. We also evaluate our algorithms on different datasets.

Keywords

Cite

@article{arxiv.1910.13511,
  title  = {A Generalization of Principal Component Analysis},
  author = {Samuele Battaglino and Erdem Koyuncu},
  journal= {arXiv preprint arXiv:1910.13511},
  year   = {2019}
}
R2 v1 2026-06-23T11:58:51.094Z