The Matrix Ridge Approximation: Algorithms and Applications
This work addresses matrix approximation challenges in machine learning, but it appears incremental as it builds on existing factorization and ridge concepts.
The paper tackles the problem of approximating symmetric positive semidefinite matrices, motivated by nonlinear machine learning methods, by introducing a matrix ridge approximation defined as an incomplete factorization plus a ridge term, and shows its potential usefulness in spectral clustering and Gaussian process regression through empirical studies.
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge approximation}. In particular, we define the matrix ridge approximation as an incomplete matrix factorization plus a ridge term. Moreover, we present probabilistic interpretations using a normal latent variable model and a Wishart model for this approximation approach. The idea behind the latent variable model in turn leads us to an efficient EM iterative method for handling the matrix ridge approximation problem. Finally, we illustrate the applications of the approximation approach in multivariate data analysis. Empirical studies in spectral clustering and Gaussian process regression show that the matrix ridge approximation with the EM iteration is potentially useful.