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Gaussian Mixture Models (GMMs) are one of the most potent parametric densitymodels used extensively in many applications. Flexibly-tied factorization ofthe covariance matrices in GMMs is a powerful approach for coping with thechallenges of common GMMs when faced with high-dimensional data and complexdensities which often demand a large number of Gaussian components. However,the expectation-maximization algorithm for fitting flexibly-tied GMMs stillencounters difficulties with streaming and very large dimensional data. Toovercome these challenges, this paper suggests the use of first-orderstochastic optimization algorithms. Specifically, we propose a new stochasticoptimization algorithm on the manifold of orthogonal matrices. Through numerousempirical results on both synthetic and real datasets, we observe thatstochastic optimization methods can outperform the expectation-maximizationalgorithm in terms of attaining better likelihood, needing fewer epochs forconvergence, and consuming less time per each epoch.

Stochastic First-Order Learning for Large-Scale Flexibly Tied Gaussian Mixture Model