# A Generalization of Principal Component Analysis

arXiv: https://arxiv.org/abs/1910.13511 · HTML: https://mlsanity.com/paper/1910.13511/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2019.

## Built on by (most cited first, 3 of 3)

- [Dynamic Embedding Size Search with Minimum Regret for Streaming Recommender System](https://mlsanity.com/paper/2308.07760/) (2023)
- [Robust Principal Component Analysis Using a Novel Kernel Related with the L1-Norm](https://mlsanity.com/paper/2105.11634/) (2021)
- [Multiplication-Avoiding Variant of Power Iteration with Applications](https://mlsanity.com/paper/2110.12065/) (2021)

## Abstract (arXiv)

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.