MAHI 2014 workshop: Methodological Aspects of Hyperspectral Imaging

Joint Blind Source Separation: Role of Diversity in Independent Decompositions
Tulay Adali, UMBC, University of Mariland, Baltimore County(US)

Data-driven methods are based on a simple generative model and hence can minimize the underlying assumptions on the data. They have emerged as promising alternatives to the traditional model-based approaches in many applications where the unknown dynamics are hard to characterize. Independent component analysis (ICA), in particular, has been a popular data-driven approach and an active area of research. Starting from a simple linear mixing model and the assumption of statistical independence, one can recover a set of linearly-mixed components to within a scaling and permutation ambiguity. It has been successfully applied to numerous data analysis problems in areas as diverse as biomedicine, communications, finance, geophysics, and remote sensing.

Most of these problems require analysis of multiple sets of data that are either of the same type as in multi-subject data, or of different types and nature as in multi-modality data. For the analysis of multiple sets of data, various possibilities arise, such as performing ICA separately on each dataset. While simple and thus attractive, such an approach faces a number of practical challenges such as ordering the estimated components due to the permutation ambiguity, and more importantly, fails to take advantage of the statistical dependence across multiple datasets while performing the decomposition. Multi-set canonical correlation analysis (MCCA), by contrast, can take second-order-statistical information among multiple datasets into account and has found wide application in data-driven analysis. A recent generalization of ICA to multiple datasets—independent vector analysis (IVA)—provides a more attractive solution to the problem by fully exploiting dependence across multiple datasets. Because of the availability of this additional diversity—statistical property—IVA provides much better performance than performing ICA separately on each dataset, and can take all order-statistics into account, not only second-order-statistics as in the case of MCCA. This talk will introduce the basic theory and methods for blind source separation—both for single and multi-set analyses—under the unifying umbrella of mutual information rate minimization and will emphasize the importance of taking different types of diversity jointly into account with various examples.