A reduced Gaussian mixture representation based on sparse modeling

Gaussian mixture is an important probability representation for the system state in many applications, especially used to model a complex density. The common drawback of Gaussian mixture representation is that the component number may grow rapidly in case with the recursive processing of Gaussian mixture. Therefore, it is extremely important to develop an efficient Gaussian Mixture Reduction (GMR) strategy to lower the increasing number of mixture components. A GMR approach based on sparse modeling is proposed in this paper. Firstly, we seek to construct a Gaussian base set by merging partial components of the original mixture, from which the components of the reduced mixture will be selected. Secondly, we aim to select a given number of components from the given Gaussian base to form the reduced mixture. By means of the idea of sparse representation, we turn the above selecting problem into a sparse modeling problem successfully in the Framework of L_1/2 regularization. Finally, we adopt the iterative half thresholding algorithm to acquire the L_1/2 regularization solution for GMR. Simulation results demonstrated the efficiency of the proposed approach.