Distributed Density Estimation Based on a Mixture of Factor Analyzers in a Sensor Network

Distributed density estimation in sensor networks has received much attention due to its broad applicability. When encountering high-dimensional observations, a mixture of factor analyzers (MFA) is taken to replace mixture of Gaussians for describing the distributions of observations. In this paper, we study distributed density estimation based on a mixture of factor analyzers. Existing estimation algorithms of the MFA are for the centralized case, which are not suitable for distributed processing in sensor networks. We present distributed density estimation algorithms for the MFA and its extension, the mixture of Student's t-factor analyzers (MtFA). We first define an objective function as the linear combination of local log-likelihoods. Then, we give the derivation process of the distributed estimation algorithms for the MFA and MtFA in details, respectively. In these algorithms, the local sufficient statistics (LSS) are calculated at first and diffused. Then, each node performs a linear combination of the received LSS from nodes in its neighborhood to obtain the combined sufficient statistics (CSS). Parameters of the MFA and the MtFA can be obtained by using the CSS. Finally, we evaluate the performance of these algorithms by numerical simulations and application example. Experimental results validate the promising performance of the proposed algorithms.