Abstract
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.
Highlights
Sensor networks are composed of tiny, intelligent sensor nodes that are deployed over a geographic region
As the mixture of factor analyzers (MFA) can handle high-dimensional observations, which are usually encountered in sensor networks, in this paper, we propose distributed density estimation algorithms for the MFA and its extension mixture of Student’s t-factor analyzers (MtFA)
We propose a distributed density estimation method base on a mixture of factor analyzers in sensor networks
Summary
Sensor networks are composed of tiny, intelligent sensor nodes that are deployed over a geographic region. In [29], a diffusion-based EM algorithm was presented for distributed estimation in unreliable sensor networks In this scenario, some nodes may be subject to data failures and report only noise. As the MFA can handle high-dimensional observations, which are usually encountered in sensor networks, in this paper, we propose distributed density estimation algorithms for the MFA and its extension MtFA. We represent these two algorithms as D-MFA and D-MtFA, respectively. In this paper, all of the parameters in the MFA or the MtFA are the same throughout the network Using this design, distributed clustering and classification can be done in arbitrary nodes after the estimation process finishes. D-tMM mixture of Student’s t-factor analyzers distributed density estimation algorithm for the MFA distributed density estimation algorithm for the MtFA combined sufficient statistics local sufficient statistics standard EM algorithm for the MFA standard EM algorithm for the MtFA non-cooperation MFA non-cooperation MtFA distributed density estimation algorithm for the GMM distributed density estimation algorithm for the Student’st-mixture model
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