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EOS SeLMA seminars

Start: 2/10/2018 - 17:30
Location: B00.35

What is happening in non-negative matrix factorization: models and algorithms

Man Shun Ang (UMons)

Given a non-negative input matrix X, the goal of the Non-negative matrix factorization (NMF) is to decompose X into two (smaller) matrices W and H such that the product WH fits X under some metric distances such as the Frobenius norm or the KL divergence. The non-negativity in NMF makes NMF finds many applications, due to the fact that the decomposed factors of NMF enjoy a higher interpretability compared to the factors obtained by other factorization methods. Despite the success of NMF, the NMF model itself is an ill-posed, underdetermined problem. Because of this, different new formulations of NMF are proposed in the past decade. This talk discusses what is going on NMF in this direction : from the classical separability condition, to the relaxed sufficiently scattered condition, minimum volume and the more. Furthermore, this talk also discusses the corresponding numerical algorithms, and their accelerated variants that are designed to tackle these new NMF formulations.

Data-driven simulation using the nuclear norm heuristic

Philippe Dreesen & Ivan Markovsky (VUB)

Applications of signal processing and control theory are classically model-based, involving a two-step procedure for modeling and design:

first a model is built from given data, and secondly, the estimated model is used for filtering, estimation, or control. Both steps typically involve optimization problems, but the combination of both is not necessarily optimal, and the modeling step often ignores the ultimate design objective. Recently, data-driven alternatives are receiving attention, which employ a direct approach combining the modeling and design into a single step. In earlier work, it was shown that data-driven signal processing problems can often be rephrased as missing data completion questions, where the signal of interest is part of a partially known low-rank mosaic-Hankel structured matrix.

In this work, we consider the exact data case and the problem of simulating a particular trajectory of the unknown data generating system. We study when the data-driven simulation problem can be solved by replacing the original structured low-rank matrix completion problem by a convex optimization problem, using the nuclear norm heuristic.

Organized by: Lieven De Lathauwer