Authors:
Miguel Almeida
1
;
Ricardo Vigário
2
and
José Bioucas-Dias
3
Affiliations:
1
Instituto Superior Técnico and Aalto University School of Science, Portugal
;
2
Aalto University School of Science, Finland
;
3
Instituto Superior Técnico, Portugal
Keyword(s):
Matrix factorization, Phase synchrony, Phase-locking, Independent component analysis, Blind source separation, Convex optimization.
Related
Ontology
Subjects/Areas/Topics:
Convex Optimization
;
ICA, PCA, CCA and other Linear Models
;
Matrix Factorization
;
Pattern Recognition
;
Theory and Methods
Abstract:
Phase Locked Matrix Factorization (PLMF) is an algorithm to perform separation of synchronous sources. Such a problem cannot be addressed by orthodox methods such as Independent Component Analysis, because synchronous sources are highly mutually dependent. PLMF separates available data into the mixing matrix and the sources; the sources are then decomposed into amplitude and phase components. Previously, PLMF was applicable only if the oscillatory component, common to all synchronized sources, was known, which is clearly a restrictive assumption. The main goal of this paper is to present a version of PLMF where this assumption is no longer needed – the oscillatory component can be estimated alongside all the other variables, thus making PLMF much more applicable to real-world data. Furthermore, the optimization procedures in the original PLMF are improved. Results on simulated data illustrate that this new approach successfully estimates the oscillatory component, together with the r
emaining variables, showing that the general problem of separation of synchronous sources can now be tackled.
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