2,081 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
Speech Denoising Using Non-Negative Matrix Factorization with Kullback-Leibler Divergence and Sparseness Constraints
Proceedings of: IberSPEECH 2012 Conference, Madrid, Spain, November 21-23, 2012.A speech denoising method based on Non-Negative Matrix Factorization (NMF) is presented in this paper. With respect to previous related works, this paper makes two contributions. First, our method does not assume a priori knowledge about the nature of the noise. Second, it combines the use of the Kullback-Leibler divergence with sparseness constraints on the activation matrix, improving the performance of similar techniques that minimize the Euclidean distance and/or do not consider any sparsification. We evaluate the proposed method for both, speech enhancement and automatic speech recognitions tasks, and compare it to conventional spectral subtraction, showing improvements in speech quality and recognition accuracy, respectively, for different noisy conditions.This work has been partially supported by the Spanish Government grants TSI-020110-2009-103 and TEC2011-26807.Publicad
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
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
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
Multilayer Structured NMF for Spectral Unmixing of Hyperspectral Images
One of the challenges in hyperspectral data analysis is the presence of mixed
pixels. Mixed pixels are the result of low spatial resolution of hyperspectral
sensors. Spectral unmixing methods decompose a mixed pixel into a set of
endmembers and abundance fractions. Due to nonnegativity constraint on
abundance fraction values, NMF based methods are well suited to this problem.
In this paper multilayer NMF has been used to improve the results of NMF
methods for spectral unmixing of hyperspectral data under the linear mixing
framework. Sparseness constraint on both spectral signatures and abundance
fractions matrices are used in this paper. Evaluation of the proposed algorithm
is done using synthetic and real datasets in terms of spectral angle and
abundance angle distances. Results show that the proposed algorithm outperforms
other previously proposed methods.Comment: 4 pages, conferenc
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
- …