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

arXiv: https://arxiv.org/abs/2306.05815 · HTML: https://mlsanity.com/paper/2306.05815/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 9 Jun 2023.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [EigenGame: PCA as a Nash Equilibrium](https://mlsanity.com/paper/2010.00554/) (2020)
- [A Simple and Efficient Algorithm for Nonlinear Model Predictive Control](https://mlsanity.com/paper/1709.06487/) (2017)
- [Exactly Robust Kernel Principal Component Analysis](https://mlsanity.com/paper/1802.10558/) (2018)
- [Functional Output Regression with Infimal Convolution: Exploring the Huber and ε-insensitive Losses](https://mlsanity.com/paper/2206.08220/) (2022)

## Built on by (most cited first, 2 of 2)

- [Accelerating Spectral Clustering under Fairness Constraints](https://mlsanity.com/paper/2506.08143/) (2025)
- [Rethinking PCA Through Duality](https://mlsanity.com/paper/2510.18130/) (2025)

## Abstract (arXiv)

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.