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PublicationMultiplicative Updates for Nonnegative Quadratic Programming(2007-01-01) Lin, Yuanqing; Sha, Fei; Lee, Daniel D; Saul, Lawrence K.Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this article, we study convex problems in quadratic programming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the global minimum. The updates have a simple closed form and do not involve any heuristics or free parameters that must be tuned to ensure convergence. Despite their simplicity, they differ strikingly in form from other multiplicative updates used in machine learning.We provide complete proofs of convergence for these updates and describe their application to problems in signal processing and pattern recognition. PublicationBlind Sparse-nonnegative (BSN) Channel Identification for Acousitic Time-Difference-of-Arrival Estimation(2007-10-01) Lin, Yuanqing; Chen, Jingdong; Lee, Daniel D; Kim, YoungmooEstimating time-difference-of-arrival (TDOA) remains a challenging task when acoustic environments are reverberant and noisy. Blind channel identification approaches for TDOA estimation explicitly model multipath reflections and have been demonstrated to be effective in dealing with reverberation. Unfortunately, existing blind channel identification algorithms are sensitive to ambient noise. This papers hows how to resolve the noise sensitivity issue by exploiting prior knowledge about an acoustic room impulse response (RIR), namely, an acoustic RIR can be modeled by a sparse-nonnegative FIR filter. This paper shows how to formulate a single-input two-output blind channel identification into a least square convex optimization, and how to incorporate the sparsity and nonnegativity priors so that the resulting optimization remains convex and can be solved efficiently. The proposed blind sparse-nonnegative (BSN) channel identification approach for TDOA estimation is not only robust to reverberation, but also robust to ambient noise, as demonstrated by simulations and experiments in real acoustic environments.