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Abstract
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In this talk, I will review some recent works on regularized matrix decomposition. Depending on the application, the matrix in consideration can be the data matrix, the latent canonical parameter matrix of an exponential family distribution, or the regression coefficient matrix of a multivariate regression. I will discuss use of various penalty functions for regularization purpose, including sparsity-inducing penalty, roughness penalty, and their combinations. Governed by the structure of the problem, the penalty can be designed for one-way or two-way regularization. I will illustrate the key ideas using applications in functional principal components analysis, biclustering, reconstruction of MEG/EEG source signals, and protein structure clustering using protein backbone angular distributions. This talk is based on joint works with Andreas Buja, Xin Gao, Seokho Lee, Mehdi Maadooliat, Haipeng Shen, Siva Tian, and Lan Zhou.
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