TY - JOUR
T1 - Sparsity and Independence
T2 - Balancing Two Objectives in Optimization for Source Separation with Application to fMRI Analysis
AU - Boukouvalas, Zois
AU - Levin-Schwartz, Yuri
AU - Calhoun, Vince D.
AU - Adalı, Tülay
N1 - Funding Information:
This work was supported in part by the NSF grants 1631838, 1539067, and 1618551, and the NIH-NIBIB grant R01EB020407.
Publisher Copyright:
© 2017 The Franklin Institute
PY - 2018/3
Y1 - 2018/3
N2 - Because of its wide applicability in various disciplines, blind source separation (BSS), has been an active area of research. For a given dataset, BSS provides useful decompositions under minimum assumptions typically by making use of statistical properties—types of diversity—of the data. Two popular types of diversity that have proven useful for many applications are statistical independence and sparsity. Although many methods have been proposed for the solution of the BSS problem that take either the statistical independence or the sparsity of the data into account, there is no unified method that can take into account both types of diversity simultaneously. In this work, we provide a mathematical framework that enables direct control over the influence of these two types of diversity and apply the proposed framework to the development of an effective ICA algorithm that can jointly exploit independence and sparsity. In addition, due to its importance in biomedical applications, we propose a new model reproducibility framework for the evaluation of the proposed algorithm. Using simulated functional magnetic resonance imaging (fMRI) data, we study the trade-offs between the use of sparsity versus independence in terms of the separation accuracy and reproducibility of the algorithm and provide guidance on how to balance these two objectives in real world applications where the ground truth is not available.
AB - Because of its wide applicability in various disciplines, blind source separation (BSS), has been an active area of research. For a given dataset, BSS provides useful decompositions under minimum assumptions typically by making use of statistical properties—types of diversity—of the data. Two popular types of diversity that have proven useful for many applications are statistical independence and sparsity. Although many methods have been proposed for the solution of the BSS problem that take either the statistical independence or the sparsity of the data into account, there is no unified method that can take into account both types of diversity simultaneously. In this work, we provide a mathematical framework that enables direct control over the influence of these two types of diversity and apply the proposed framework to the development of an effective ICA algorithm that can jointly exploit independence and sparsity. In addition, due to its importance in biomedical applications, we propose a new model reproducibility framework for the evaluation of the proposed algorithm. Using simulated functional magnetic resonance imaging (fMRI) data, we study the trade-offs between the use of sparsity versus independence in terms of the separation accuracy and reproducibility of the algorithm and provide guidance on how to balance these two objectives in real world applications where the ground truth is not available.
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U2 - 10.1016/j.jfranklin.2017.07.003
DO - 10.1016/j.jfranklin.2017.07.003
M3 - Article
AN - SCOPUS:85025820167
VL - 355
SP - 1873
EP - 1887
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
SN - 0016-0032
IS - 4
ER -