Results 1 - 10 of 2,263

Algorithms for Non-negative Matrix Factorization

by Daniel D. Lee, H. Sebastian Seung - In NIPS , 2001
"... Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minim ..."
Abstract - Cited by 1246 (5 self) - Add to MetaCart
Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown

Non-negative matrix factorization with sparseness constraints,”

by Patrik O Hoyer , Patrik Hoyer@helsinki , Fi - Journal of Machine Learning Research, , 2004
"... Abstract 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 sho ..."
Abstract - Cited by 498 (0 self) - Add to MetaCart
Abstract 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

Factoring wavelet transforms into lifting steps

by Ingrid Daubechies, Wim Sweldens - J. FOURIER ANAL. APPL , 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
Abstract - Cited by 584 (8 self) - Add to MetaCart
. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is well-known to algebraists (and expressed by the formula); it is also used in linear systems theory in the electrical engineering community. We

Monaural sound source separation by nonnegative matrix factorization with temporal continuity and sparseness criteria

by Tuomas Virtanen - IEEE Trans. On Audio, Speech and Lang. Processing , 2007
"... Abstract—An unsupervised learning algorithm for the separation of sound sources in one-channel music signals is presented. The algorithm is based on factorizing the magnitude spectrogram of an input signal into a sum of components, each of which has a fixed magnitude spectrum and a time-varying gain ..."
Abstract - Cited by 189 (30 self) - Add to MetaCart
with independent subspace analysis and basic nonnegative matrix factorization, which are based on the same linear model. According to these simulations, the proposed method enables a better separation quality than the previous algorithms. Especially, the temporal continuity criterion improved the detection

Projected gradient methods for Nonnegative Matrix Factorization

by Chih-jen Lin - Neural Computation , 2007
"... Non-negative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this paper, we propose two proj ..."
Abstract - Cited by 282 (2 self) - Add to MetaCart
Non-negative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this paper, we propose two

Non-negative matrix factorization for polyphonic music transcription

by Paris Smaragdis, Judith C. Brown - IN PROC. IEEE WORKSHOP APPLICATIONS OF SIGNAL PROCESSING TO AUDIO AND ACOUSTICS , 2003
"... In this paper we present a methodology for analyzing polyphonic musical passages comprised by notes that exhibit a harmonically fixed spectral profile (such as piano notes). Taking advantage of this unique note structure we can model the audio content of the musical passage by a linear basis transfo ..."
Abstract - Cited by 240 (14 self) - Add to MetaCart
transform and use non-negative matrix decomposition methods to estimate the spectral profile and the temporal information of every note. This approach results in a very simple and compact system that is not knowledge based, but rather learns notes by observation.

Online learning for matrix factorization and sparse coding

by Julien Mairal, Francis Bach, Jean Ponce, Guillermo Sapiro , 2010
"... Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set in order to ad ..."
Abstract - Cited by 330 (31 self) - Add to MetaCart
to adapt it to specific data. Variations of this problem include dictionary learning in signal processing, non-negative matrix factorization and sparse principal component analysis. In this paper, we propose to address these tasks with a new online optimization algorithm, based on stochastic approximations

Algorithms and applications for approximate nonnegative matrix factorization

by Michael W. Berry, Murray Browne, Amy N. Langville, V. Paul Pauca, Robert J. Plemmons - Computational Statistics and Data Analysis , 2006
"... In this paper we discuss the development and use of low-rank approximate nonnegative matrix factorization (NMF) algorithms for feature extraction and identification in the fields of text mining and spectral data analysis. The evolution and convergence properties of hybrid methods based on both spars ..."
Abstract - Cited by 204 (8 self) - Add to MetaCart
In this paper we discuss the development and use of low-rank approximate nonnegative matrix factorization (NMF) algorithms for feature extraction and identification in the fields of text mining and spectral data analysis. The evolution and convergence properties of hybrid methods based on both

When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts?

by David Donoho, Victoria Stodden
"... We interpret non-negative matrix factorization geometrically, as the problem of finding a simplicial cone which contains a cloud of data points and which is contained in the positive orthant. We show that under certain conditions, basically requiring that some of the data are spread across the faces ..."
Abstract - Cited by 200 (1 self) - Add to MetaCart
We interpret non-negative matrix factorization geometrically, as the problem of finding a simplicial cone which contains a cloud of data points and which is contained in the positive orthant. We show that under certain conditions, basically requiring that some of the data are spread across

On the equivalence of nonnegative matrix factorization and spectral clustering

by Chris Ding, Xiaofeng He, Horst D. Simon - in SIAM International Conference on Data Mining , 2005
"... Current nonnegative matrix factorization (NMF) deals with X = FG T type. We provide a systematic analysis and extensions of NMF to the symmetric W = HH T, and the weighted W = HSHT. We show that (1) W = HHT is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2) X ..."
Abstract - Cited by 159 (20 self) - Add to MetaCart
Current nonnegative matrix factorization (NMF) deals with X = FG T type. We provide a systematic analysis and extensions of NMF to the symmetric W = HH T, and the weighted W = HSHT. We show that (1) W = HHT is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2
Results 1 - 10 of 2,263