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Project

Taming Nonconvexity in Structured Low-Rank Optimization.

Recent technological advances have led to a dramatic rate of
acquired data in many branches of sciences and engineering. A
natural way of mining valuable features out of these data is to
represent them as lower dimensional objects that allow intuitive
interpretation by domain-specific experts. Nonnegative matrix
factorization (NMF) is a popular dimensionality reduction tool where a
data matrix is decomposed to two (or more) nonnegative matrices
with much smaller dimensions to extract valuable information. The
main bottleneck is the need to efficiently and rapidly solve a hugescale
nonconvex optimization problem. This project aims to (i)
introduce a new class of structured low-rank models called
Generalized NMF (GNMF), (ii) design algorithms and highperformance
software for solving large-scale optimization problems
appearing in GNMF applications and (iii) apply GNMF in data science
and biomedicine. We will follow the advancements of the recent idea
of the PI on Bregman proximal envelopes, where the developed
algorithms are supported with strong convergence guarantees and
are ideal for parallel and distributed computations using state-of-the
art high-performance computers. The project has strong potential to
lead to high impact results such as the discovery of new pan-cancer
genes and new insights into scientific collaboration based on merging
bibliometric data.

Date:1 Jan 2022 →  Today
Keywords:Nonconvex Optimization, Structured low-rank matrix optimization, Generalized nonnegative matrix factorization
Disciplines:Data visualisation and imaging, Operations research and mathematical programming, Control systems, robotics and automation not elsewhere classified, Numerical computation, Signal processing