We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: On-line learning with a simple square loss and finding a symmetric positiv...

A positive definite completion problem pertains to determining whether the unspecified positions of a partial (or incomplete) matrix can be completed in a desired subclass of positive definite matrices. In this paper we study an important and new class of positive definite completion problems where the desired subclasses are the spaces of covariance and inverse-covariance matrices of probabilis...

The Line Sum Scaling problem for a nonnegative matrix A is to find positive definite diagonal matrices Y , Z which result in prescribed row and column sums of the scaled matrix Y AZ. The Matrix Balancing problem for a nonnegative square matrix A is to find a positive definite diagonal matrix X such that the row sums in the scaled matrix XAX are equal to the corresponding column sums. We demonst...

Logic programs are an important knowledge representation tool. In many cases, definite logic programs are too restricted to formalize problems intuitively. Therefore definite logic programs have been extended in several ways by additional syntactic constructs such as negation and disjunction. A very expressive program class are generalized logic programs. Their rules may contain any quantifier ...

In this paper we outline a new swarm intelligence based approach to the problem of training support vector machines with non positive definite kernels. Past approaches using particle swarm optimizers have been shown to compare poorly with other evolutionary computation based methods. In this paper, we describe a new heterogeneous particle swarm optimizer, specifically tailored for the training ...