A Dual Formulation for Probabilistic Principal Component Analysis
This work provides a theoretical extension for kernel-based dimensionality reduction, which is incremental as it builds on existing probabilistic PCA methods.
The paper tackles the problem of extending Probabilistic Principal Component Analysis to Hilbert spaces by deriving a dual formulation, enabling a generative framework for kernel methods that includes Kernel Principal Component Analysis, and demonstrates its application on toy and real datasets.
In this paper, we characterize Probabilistic Principal Component Analysis in Hilbert spaces and demonstrate how the optimal solution admits a representation in dual space. This allows us to develop a generative framework for kernel methods. Furthermore, we show how it englobes Kernel Principal Component Analysis and illustrate its working on a toy and a real dataset.