473 research outputs found
Parallel Algorithms for Constrained Tensor Factorization via the Alternating Direction Method of Multipliers
Tensor factorization has proven useful in a wide range of applications, from
sensor array processing to communications, speech and audio signal processing,
and machine learning. With few recent exceptions, all tensor factorization
algorithms were originally developed for centralized, in-memory computation on
a single machine; and the few that break away from this mold do not easily
incorporate practically important constraints, such as nonnegativity. A new
constrained tensor factorization framework is proposed in this paper, building
upon the Alternating Direction method of Multipliers (ADMoM). It is shown that
this simplifies computations, bypassing the need to solve constrained
optimization problems in each iteration; and it naturally leads to distributed
algorithms suitable for parallel implementation on regular high-performance
computing (e.g., mesh) architectures. This opens the door for many emerging big
data-enabled applications. The methodology is exemplified using nonnegativity
as a baseline constraint, but the proposed framework can more-or-less readily
incorporate many other types of constraints. Numerical experiments are very
encouraging, indicating that the ADMoM-based nonnegative tensor factorization
(NTF) has high potential as an alternative to state-of-the-art approaches.Comment: Submitted to the IEEE Transactions on Signal Processin
Non-negative mixtures
This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.2
Sparse and Non-Negative BSS for Noisy Data
Non-negative blind source separation (BSS) has raised interest in various
fields of research, as testified by the wide literature on the topic of
non-negative matrix factorization (NMF). In this context, it is fundamental
that the sources to be estimated present some diversity in order to be
efficiently retrieved. Sparsity is known to enhance such contrast between the
sources while producing very robust approaches, especially to noise. In this
paper we introduce a new algorithm in order to tackle the blind separation of
non-negative sparse sources from noisy measurements. We first show that
sparsity and non-negativity constraints have to be carefully applied on the
sought-after solution. In fact, improperly constrained solutions are unlikely
to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA
(non-negative Generalized Morphological Component Analysis), makes use of
proximal calculus techniques to provide properly constrained solutions. The
performance of nGMCA compared to other state-of-the-art algorithms is
demonstrated by numerical experiments encompassing a wide variety of settings,
with negligible parameter tuning. In particular, nGMCA is shown to provide
robustness to noise and performs well on synthetic mixtures of real NMR
spectra.Comment: 13 pages, 18 figures, to be published in IEEE Transactions on Signal
Processin
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