Diversity in Independent Component and Vector Analyses: Identifiability, algorithms, and applications in medical imaging

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dc.contributor.authorAdali, Tulay
dc.contributor.authorAnderson, Matthew
dc.contributor.authorFu, Geng-Shen
dc.date.accessioned2019-02-08T18:32:15Z
dc.date.available2019-02-08T18:32:15Z
dc.date.issued2014-04-07
dc.description.abstractStarting with a simple generative model and the assumption of statistical independence of the underlying components, independent component analysis (ICA) decomposes a given set of observations by making use of the diversity in the data, typically in terms of statistical properties of the signal. Most of the ICA algorithms introduced to date have considered one of the two types of diversity: non-Gaussianity?i.e., higher-order statistics (HOS)?or, sample dependence. A recent generalization of ICA, independent vector analysis (IVA), generalizes ICA to multiple data sets and adds the use of one more diversity, dependence across multiple data sets for achieving an independent decomposition, jointly across multiple data sets. Finally, both ICA and IVA, when implemented in the complex domain, enjoy the addition of yet another type of diversity, noncircularity of the sources?underlying components. Mutual information rate provides a unifying framework such that all these statistical properties?types of diversity?can be jointly taken into account for achieving the independent decomposition. Most of the ICA methods developed to date can be cast as special cases under this umbrella, as well as the more recently developed IVA methods. In addition, this formulation allows us to make use of maximum likelihood theory to study large sample properties of the estimator, derive the Cramer-Rao lower bound(CRLB) and determine the conditions for the identifiability of the ICA and IVA models. In this overview article, we first present ICA, and then its generalization to multiple data sets, IVA, both using mutual information rate, present conditions for the identifiability of the given linear mixing model and derive the performance bounds. We address how various methods fall under this umbrella and give examples of performance for a few sample algorithms compared with the performance bound. We then discuss the importance of approaching the performance bound depending on the goal, and use medical image analysis as the motivating example.en_US
dc.description.sponsorshipThis work was supported by the National Science Foundation (grants NSF-IIS 1017718 and NSF-CCF 1117056). The authors would like to thank Jonathan Laney for generating the fMRI analysis results using IVA.en_US
dc.description.urihttps://ieeexplore.ieee.org/document/6784026/authors#authorsen_US
dc.format.extent16 pagesen_US
dc.genrejournal articles postprintsen_US
dc.identifierdoi:10.13016/m24uql-ulsm
dc.identifier.citationTulay Adali , Matthew Anderson, Geng-Shen Fu, Diversity in Independent Component and Vector Analyses: Identifiability, algorithms, and applications in medical imaging , IEEE Signal Processing Magazine ( Volume: 31 , Issue: 3 , May 2014) , DOI: 10.1109/MSP.2014.2300511en_US
dc.identifier.urihttps://doi.org/10.1109/MSP.2014.2300511
dc.identifier.urihttp://hdl.handle.net/11603/12748
dc.language.isoen_USen_US
dc.publisherIEEEen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Computer Science and Electrical Engineering Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Student Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.rights© 2014 IEEE
dc.subjecthigher order statisticsen_US
dc.subjectindependent component analysisen_US
dc.subjectmatrix decompositionen_US
dc.subjectmaximum likelihood estimationen_US
dc.subjectmixture modelsen_US
dc.subjectvectorsen_US
dc.subjectsignal processing algorithmsen_US
dc.subjectmedical image processingen_US
dc.subjectmutual informationen_US
dc.subjectsource separationen_US
dc.subjectstatistical analysisen_US
dc.subjectMachine Learning for Signal Processing Laben_US
dc.titleDiversity in Independent Component and Vector Analyses: Identifiability, algorithms, and applications in medical imagingen_US
dc.typeTexten_US

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