Topic: Detection of Sources in Non-negative Blind Source
Separation by Minimum Description Length Criterion

Speaker: 祁忠勇 (Professor, Institute of Communications
Engineering&Department of Electrical Engineering)

Location: Delta R216

Time&Data: 2:30~4:30, 6/09

Abstract:

While non-negative blind source separation (nBSS) has found many
successful applications in science and engineering, model order
selection, determining the number of sources, remains a critical yet
unresolved problem. Various model order selection methods have been
proposed and applied to real-world datasets but with limited success,
with both order over- and under- estimation reported. By studying
existing schemes, we have found that the unsatisfactory results are
mainly due to invalid assumptions, model oversimplification,
subjective thresholding, and/or to assumptions made solely for
mathematical convenience. Building on our earlier work that
reformulated model order selection for nBSS with more realistic
assumptions and models, in this talk, we introduce a newly and
formally revised model order selection criterion rooted in the minimum
description length (MDL) principle. Adopting widely-invoked
assumptions for achieving a unique nBSS solution, we consider the
mixing matrix as consisting of deterministic unknowns, with the source
signals following a multivariate Dirichlet distribution. We derive a
computationally efficient, stochastic algorithm to obtain approximate
maximum-likelihood estimates of model parameters and apply Monte Carlo
integration to determine the description length. Our modeling and
estimation strategy exploits the characteristic geometry of the data
simplex in nBSS. We validate our nBSS-MDL criterion through extensive
simulation studies and on four real-world datasets, demonstrating its
strong performance and general applicability to nBSS. The proposed
nBSS-MDL criterion consistently detects the true number of sources, in
all of our case studies.