In the analysis of a recently proposed distributed estimation algorithm based on the Kalman ltering and on gossip iterations, we needed to apply a new inequality which is valid for i.i.d. matrix valued random processes. This inequality can be useful in the analysis of the convergence rate of general jump Markov linear systems. In this paper we present this inequality. This is based on the theor...

We formulate multi-input multi-output proportional integral derivative controller design as an optimization problem that involves nonconvex quadratic matrix inequalities. We propose a simple method that replaces the nonconvex matrix inequalities with a linear matrix inequality restriction, and iterates to convergence. This method can be interpreted as a matrix extension of the convex–concave pr...

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...