Browsing by Subject "independent component analysis"
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Item Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety(IEEE, 2011-07-25) Adali, Tulay; Schreier, Peter J.; Scharf, Louis L.Complex-valued signals occur in many areas of science and engineering and are thus of fundamental interest. In the past, it has often been assumed, usually implicitly, that complex random signals are proper or circular. A proper complex random variable is uncorrelated with its complex conjugate, and a circular complex random variable has a probability distribution that is invariant under rotation in the complex plane. While these assumptions are convenient because they simplify computations, there are many cases where proper and circular random signals are very poor models of the underlying physics. When taking impropriety and noncircularity into account, the right type of processing can provide significant performance gains. There are two key ingredients in the statistical signal processing of complex-valued data: 1) utilizing the complete statistical characterization of complex-valued random signals; and 2) the optimization of real-valued cost functions with respect to complex parameters. In this overview article, we review the necessary tools, among which are widely linear transformations, augmented statistical descriptions, and Wirtinger calculus. We also present some selected recent developments in the field of complex-valued signal processing, addressing the topics of model selection, filtering, and source separation.Item Diversity in Independent Component and Vector Analyses: Identifiability, algorithms, and applications in medical imaging(IEEE, 2014-04-07) Adali, Tulay; Anderson, Matthew; Fu, Geng-ShenStarting 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.Item Independent Component Analysis for Trustworthy Cyberspace during High Impact Events: An Application to Covid-19(2020-06-30) Boukouvalas, Zois; Mallinson, Christine; Crothers, Evan; Japkowicz, Nathalie; Piplai, Aritran; Mittal, Sudip; Joshi, Anupam; Adalı, TülaySocial media has become an important communication channel during high impact events, such as the COVID-19 pandemic. As misinformation in social media can rapidly spread, creating social unrest, curtailing the spread of misinformation during such events is a significant data challenge. While recent solutions that are based on machine learning have shown promise for the detection of misinformation, most widely used methods include approaches that rely on either handcrafted features that cannot be optimal for all scenarios, or those that are based on deep learning where the interpretation of the prediction results is not directly accessible. In this work, we propose a data-driven solution that is based on the ICA model, such that knowledge discovery and detection of misinformation are achieved jointly. To demonstrate the effectiveness of our method and compare its performance with deep learning methods, we developed a labeled COVID-19 Twitter dataset based on socio-linguistic criteria.