Non-negative Matrix Factor Deconvolution; Extracation of Multiple Sound Sources from Monophonic Inputs International Symposium on Independent Component Analysis and Blind Source Separation, ICA 2004 Paris Smaragdis / Mitsubishi Electric Research Laboratori Presenter: Jain_De ,Lee
Non-negative Matrix Factor Deconvolution; Extracation of Multiple Sound Sources from Monophonic Inputs International Symposium on Independent Component.
Jan 29, 2016
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Non-negative Matrix Factor Deconvolution;Extracation of Multiple Sound Sources from Monophonic Inputs
International Symposium on Independent Component Analysis and Blind Source Separation, ICA 2004
Paris Smaragdis / Mitsubishi Electric Research Laboratories
Presenter: Jain_De ,Lee
Outline
• Introduction
• Non-negative Matrix Factorization
• Non-negative Matrix Factor Deconvolution
• Conclusions
Introduction
• Theory of The Origin
• An extension to the Non-Negative Matrix Factorization algorithm – Identifying components with temporal
structure
Paatero (1997)
Lee&Seung (1999)
Non-negative Matrix Factorization
• The Original Formulation of NMF
NRRMNM HWV
[W] : Basis Functions Matrix
[H] :Time Weights Matrix
Non-negative Matrix Factorization
• The Cost Function
• Multiplicative Update Algorithm
1
T
T
WHWV
WHH T
T
H
HHWV
WW
1
F
WHVWH
VVD )ln(
Non-negative Matrix Factorization
• NMF for Sound Object Extraction
STFT
Non-negative Matrix Factorization
Non-negative Matrix Factor Deconvolution
• The Formulation of NMFD
• The Operator Shifts The Columns
WHV
1
0
T
t
t
t HWV
987
654
321
A
870
540
2101
A
700
400
1002
A ….
i
)(
Non-negative Matrix Factor Deconvolution
• The Cost Function
• The Update Rules
F
VV
VD
ln
1
Tt
t
Tt
W
VW
HH Tt
Tt
tt
H
HV
WW
1
10 Tt
1
0
T
t
t
t HW， where
，
Non-negative Matrix Factor Deconvolution
Non-negative Matrix Factor Deconvolution
• In this example the drum sounds exhibit some overlap at both time and frequency
Three types of drum sounds present into the scece Sampled at 11.025 kHz 256-point DFTs which were overlapping by 128-points Performed for 3 basis functions
Non-negative Matrix Factor Deconvolution
• Reconstruction
tT
t
jtj HWV
1
0
)(
Conclusions
• Pinpointed some of the shortcomings of conventional NMF when analyzing temporal patterns and presented an extension
• Spectral bases have been used on spectrograms to extract sound objects from single channel sound scenes
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