  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.
