Cécile Hautecoeur

joint work with François Glineur

Nonnegative matrix factorization over polynomial signals via a sum-of-squares approach

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique successfully used for analysis of discrete data, such as images. It is a discrete process by nature while the analyzed signals may be continuous. The aim of this work is to extend NMF to deal with continuous signals, avoiding a priori discretization. In other words, we seek a small basis of nonnegative signals capable of additively reconstructing a large dataset. We propose a new method to compute NMF for polynomials or splines using an alternating minimization scheme relying on sum-of-squares representation.

Fei Wang

Noisy Euclidean Distance Matrix Completion with A Single Missing Node

We present several solution techniques for the noisy single source localization problem,i.e.,~the Euclidean distance matrix completion problem with a single missing node to locate under noisy data. For the case that the sensor locations are fixed, we show that this problem is implicitly convex, and we provide a purification algorithm along with the SDP relaxation to solve it efficiently and accurately. For the case that the sensor locations are relaxed, we study a model based on facial reduction. We present several approaches to solve this problem efficiently and compare their performance.