1,856 research outputs found
Non-negative matrix factorization with sparseness constraints
Non-negative matrix factorization (NMF) is a recently developed technique for
finding parts-based, linear representations of non-negative data. Although it
has successfully been applied in several applications, it does not always
result in parts-based representations. In this paper, we show how explicitly
incorporating the notion of `sparseness' improves the found decompositions.
Additionally, we provide complete MATLAB code both for standard NMF and for our
extension. Our hope is that this will further the application of these methods
to solving novel data-analysis problems
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
Learning image components for object recognition
In order to perform object recognition it is necessary to learn representations of the underlying components of images. Such components correspond to objects, object-parts, or features. Non-negative matrix factorisation is a generative model that has been specifically proposed for finding such meaningful representations of image data, through the use of non-negativity constraints on the factors. This article reports on an empirical investigation of the performance of non-negative matrix factorisation algorithms. It is found that such algorithms need to impose additional constraints on the sparseness of the factors in order to successfully deal with occlusion. However, these constraints can themselves result in these algorithms failing to identify image components under certain conditions. In contrast, a recognition model (a competitive learning neural network algorithm) reliably and accurately learns representations of elementary image features without such constraints
Non-negative sparse coding
Non-negative sparse coding is a method for decomposing multivariate data into
non-negative sparse components. In this paper we briefly describe the
motivation behind this type of data representation and its relation to standard
sparse coding and non-negative matrix factorization. We then give a simple yet
efficient multiplicative algorithm for finding the optimal values of the hidden
components. In addition, we show how the basis vectors can be learned from the
observed data. Simulations demonstrate the effectiveness of the proposed
method
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
Block Coordinate Descent for Sparse NMF
Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data
analysis. An important variant is the sparse NMF problem which arises when we
explicitly require the learnt features to be sparse. A natural measure of
sparsity is the L norm, however its optimization is NP-hard. Mixed norms,
such as L/L measure, have been shown to model sparsity robustly, based
on intuitive attributes that such measures need to satisfy. This is in contrast
to computationally cheaper alternatives such as the plain L norm. However,
present algorithms designed for optimizing the mixed norm L/L are slow
and other formulations for sparse NMF have been proposed such as those based on
L and L norms. Our proposed algorithm allows us to solve the mixed norm
sparsity constraints while not sacrificing computation time. We present
experimental evidence on real-world datasets that shows our new algorithm
performs an order of magnitude faster compared to the current state-of-the-art
solvers optimizing the mixed norm and is suitable for large-scale datasets
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