id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_zpfso6pk3vf5df7625v6vawp2e	Xia Hong	Estimating the square root of probability density function on Riemannian manifold	2018	21	.pdf	application/pdf	5356	888	73	The importance of probability density function (PDF) is evidenced by intensive theoretic researches and many data analysis and pattern recognition applications [McLachlan and Peel, 2000, Silverman, 1986, Duda and Hart, 1973, Chen et al., 2010, nonlinear optimisation process requiring extensive computation, while the EM algorithm for Gaussian mixture models enjoys an explicit iterative form [Bilmes, 1998]. recently we have introduced Riemannian trust-region (RTR) algorithm for sparse finite mixture model based on minimal integrated square error criterion [Hong et al., gradient algorithm [Hager and Zhang, 2006] to optimization problems over Riemannian manifolds [Boumal et al., 2014]. Algorithm 3 Proposed estimator for the square root of probability density function Estimating the Square Root of Probability Density Function on Riemannian Manifold Estimating the Square Root of Probability Density Function on Riemannian Manifold Estimating the Square Root of Probability Density Function on Riemannian Manifold Estimating the Square Root of Probability Density Function on Riemannian Manifold	./cache/work_zpfso6pk3vf5df7625v6vawp2e.pdf	./txt/work_zpfso6pk3vf5df7625v6vawp2e.txt