Nonnegative Matrix Factorization (NMF) is a promising relaxation technique for clustering analysis. However, conventional NMF methods that directly approximate the pairwise similarities using the least square error often yield mediocre performance for data in curved manifolds because they can capture only the immediate similarities between data samples. Here we propose a new NMF clustering meth...

The adoption of the stress-majorization method frommulti-dimensional scaling into graph layout has provided an improved mathematical basis and better convergence properties for so-called “force-directed placement” techniques. In this paper we give an algorithm for augmenting such stress-majorization techniques with orthogonal ordering constraints and we demonstrate several graphdrawing applicat...

In recent years, tensor completion problem has received a significant amount of attention in computer vision, data mining and neuroscience. It is the higher order generalization of matrix completion. And these can be solved by the convex relaxation which minimizes the tensor nuclear norm instead of the n-rank of the tensor. In this paper, we introduce the weighted nuclear norm for tensor and de...

There has been much discussion in the literature about rival measures of classical polarization in three dimensions. We gather and compare the various proposed measures of polarization, creating a geometric representation of the polarization state space in the process. We use majorization, previously used in quantum information, as a criterion to establish a partial ordering on the polarization...

We develop majorization results that characterize changes in eigenvector components of a graph’s adjacency matrix when its topology is changed. Specifically, for general (weighted, directed) graphs, we characterize changes in dominant eigenvector components for single-row and multi-row incrementations. We also show that topology changes can be tailored to set ratios between the components of th...

Abstract. In this paper, a complete solution of a problem involving generalized majorization of partitions is given: for two pairs of partitions (d, a) and (c,b) necessary and sufficient conditions for the existence of a partition g that is majorized by both pairs is determined. The obtained conditions are explicit, the solution is constructive and it uses novel techniques and indices. Although...

In this work we continue the nonsmooth analysis of absolutely symmetric functions of the singular values of a real rectangular matrix. Absolutely symmetric functions are invariant under permutations and sign changes of its arguments. We extend previous work on subgradients to analogous formulae for the proximal subdifferential and Clarke subdifferential when the function is either locally Lipsc...