We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, defined as wellconnected subsets of vertices. The decomposition is based on a statistical description which encourages clusters to be well connected and few...

In this paper we consider the expected value function of a stochastic simple recourse program with random technology matrix and integer variables in the second stage. Due to its separability the analysis is straightforward. Conditions for finiteness, continuity, Lipschitz continuity and differentiability are derived by conditioning upon the technology matrix. The corresponding results for a fix...

Nonnegative Matrix Factorization has been proved to be valuable in many fields of data mining, especially in unsupervised learning. In this paper, we will briefly review its variations and applications in image processing, data clustering, semi-supervised clustering, bi-clustering (co-clustering) and financial data mining. Note that we cannot cover all the interesting works on NMF, but generall...

Singular Value Decomposition (SVD) is a useful tool in Functional Data Analysis (FDA). Compared to Principal Component Analysis (PCA), SVD is more fundamental, because SVD simultaneously provides the PCAs in both row and column spaces. We compare SVD and PCA from the FDA view point, and extend the usual SVD to variations by considering different centerings. A generalized scree plot is proposed ...