Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast
  Algorithms
Francesco Tonin Alex Lambert Panagiotis Patrinos Johan A. K. Suykens
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.