A Dual Formulation for Probabilistic Principal Component Analysis

PCA, but rather in another model based on similar In this paper, we characterize Probabilistic Principal principles. Component Analysis in Hilbert spaces and demonstrate how the optimal solution admits a More recently, Restricted Kernel Machines (Suykens, 2017) representation in dual space. This allows us to develop opened a new door for a probabilistic version of PCA both a generative framework for kernel methods. in primal and dual. They essentially use the Fenchel-Young Furthermore, we show how it englobes Kernel inequality on a variational formulation of KPCA (Suykens Principal Component Analysis and illustrate its et al., 2003; Alaíz et al., 2018) to obtain an energy function, working on a toy and a real dataset.