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Non-negative dyadic data, that is data representing observations which relate two finite sets of objects, appear in several domain applications, such as text-mining-based information retrieval, collaborative filtering and recommender systems, micro-array analysis and computer vision. Discovering latent subgroups among data is a fundamental task to be performed on dyadic data. In this context, clustering and co-clustering techniques are relevant tools for extracting and representing latent information in high dimensional data. Recently, Non-negative Matrix Factorizations attracted a great interest as clustering methods, due to their capability of performing a parts-based decomposition of data. In this paper, we focus our attention on how NMF with additional constraints can be properly applied for co-clustering non-negative dyadic data. In particular, we present a process which aims at enhancing the performance of 3-factors NMF as a co-clustering method, by identifying a clearer correlation structure represented by the block matrix. Experimental evaluation performed on some common datasets, by applying the proposed approach on two different NMF algorithms, shows that, in most cases, the quality of the obtained clustering increases, especially in terms of average inter-cluster similarity. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider numerical methods for computing functions of matrices being Hamiltonian and skew-symmetric. Analytic functions of this kind of matrices (i.e., exponential and rational functions) appear in the numerical solutions of ortho-symplectic matrix differential systems when geometric integrators are involved. The main idea underlying the presented techniques is to exploit the special block structure of a Hamiltonian and skew-symmetric matrix to gain a cheaper computation of the functions. First, we will consider an approach based on the numerical solution of structured linear systems and then another one based on the Schur decomposition of the matrix. Splitting techniques are also considered in order to reduce the computational cost. Several numerical tests and comparison examples are shown. [Copyright &y& Elsevier]