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