Sparse density estimation on multinomial manifold combining local component analysis

Hong, X. ORCID: https://orcid.org/0000-0002-6832-2298 and Gao, J. (2015) Sparse density estimation on multinomial manifold combining local component analysis. In: 2015 International Joint Conference on Neural Networks (IJCNN), 12-17, July, 2015, Killarney, Ireland.

Abstract/Summary

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.