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Sensors 2015, 15(8), 19047-19068; doi:10.3390/s150819047

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

1
College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
2
Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
3
School of Information Science and Engineering, Southeast University, Nanjing 210096, China
*
Author to whom correspondence should be addressed.
Academic Editor: Leonhard M. Reindl
Received: 27 May 2015 / Revised: 27 July 2015 / Accepted: 30 July 2015 / Published: 5 August 2015
(This article belongs to the Section Sensor Networks)
View Full-Text   |   Download PDF [388 KB, uploaded 5 August 2015]   |  

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. View Full-Text
Keywords: distributed density estimation; mixture of factor analyzers; mixture of Student’s t-factor analyzers; sensor network distributed density estimation; mixture of factor analyzers; mixture of Student’s t-factor analyzers; sensor network
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Wei, X.; Li, C.; Zhou, L.; Zhao, L. Distributed Density Estimation Based on a Mixture of Factor Analyzers in a Sensor Network. Sensors 2015, 15, 19047-19068.

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