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.

翻译：本文旨在通过凸函数差分的对偶化重新审视核主成分分析（KPCA）。该方法自然地扩展了KPCA至多种目标函数，并导出了高效的基于梯度的算法，避免了Gram矩阵昂贵的奇异值分解。特别地，我们考虑了可表示为Moreau包络的目标函数，展示了如何在统一框架内提升鲁棒性和稀疏性。所提方法在合成数据和真实世界基准测试上进行了评估，结果表明KPCA训练时间显著加快，并在鲁棒性和稀疏性方面展现了优势。