Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithms
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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.
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
5 of 35 references.
References · 5
- 2015Deep Residual Learning for Image Recognitioncited by 52,096
- 2020EigenGame: PCA as a Nash Equilibriumcited by 39
- 2017A Simple and Efficient Algorithm for Nonlinear Model Predictive Controlcited by 7
- 2018Exactly Robust Kernel Principal Component Analysiscited by 7
- 2022Functional Output Regression with Infimal Convolution: Exploring the Huber and ε-insensitive Lossescited by 1
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Citing papers per year: 2025: 2.
2 papers.
- 2025Accelerating Spectral Clustering under Fairness Constraintscited by 0
- 2025Rethinking PCA Through Dualitycited by 0
- 2025Rethinking PCA Through Duality20 Oct 2025
- 2025Accelerating Spectral Clustering under Fairness Constraints9 Jun 2025