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 [W] : Basis Functions Matrix [H] :Time Weights Matrix

Non-negative Matrix Factorization The Cost Function Multiplicative Update Algorithm

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 ….

Non-negative Matrix Factor Deconvolution The Cost Function The Update Rules ， where ，

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 kHz  256-point DFTs which were overlapping by 128-points  Performed for 3 basis functions

Non-negative Matrix Factor Deconvolution Reconstruction

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