Convolutive Non-Negative Matrix Factorisation with a Sparseness Constraint

Discovering a representation which allows auditory data to be parsimoniously represented is useful for many machine learning and signal processing tasks. Such a representation can be constructed by non-negative matrix factorisation (NMF), a method for finding parts-based representations of non-negative data. We present an extension to NMF that is convolutive and includes a sparseness constraint. In combination with a spectral magnitude transform, this method discovers auditory objects and their associated sparse activation patterns.

[1]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[2]  P. Paatero,et al.  Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values† , 1994 .

[3]  David J. Field,et al.  What Is the Goal of Sensory Coding? , 1994, Neural Computation.

[4]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[5]  R. Lambert Multichannel blind deconvolution: FIR matrix algebra and separation of multipath mixtures , 1996 .

[6]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis , 1997, Neural Computation.

[7]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[8]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[9]  D. Donoho,et al.  Atomic Decomposition by Basis Pursuit , 2001 .

[10]  E. Oja,et al.  Independent Component Analysis , 2013 .

[11]  Barak A. Pearlmutter,et al.  Blind Source Separation by Sparse Decomposition in a Signal Dictionary , 2001, Neural Computation.

[12]  Patrik O. Hoyer,et al.  Non-negative sparse coding , 2002, Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing.

[13]  Tuomas Virtanen,et al.  Sound Source Separation Using Sparse Coding with Temporal Continuity Objective , 2003, ICMC.

[14]  Victoria Stodden,et al.  When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts? , 2003, NIPS.

[15]  Mark D. Plumbley,et al.  Polyphonic music transcription by non-negative sparse coding of power spectra , 2004 .

[16]  Bruno A Olshausen,et al.  Sparse coding of sensory inputs , 2004, Current Opinion in Neurobiology.

[17]  Paris Smaragdis,et al.  Non-negative Matrix Factor Deconvolution; Extraction of Multiple Sound Sources from Monophonic Inputs , 2004, ICA.

[18]  Derry Fitzgerald,et al.  Sound Source Separation Using Shifted Non-Negative Tensor Factorisation , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.