Exponentially embedded families for multimodal sensor processing

The exponential embedding of two or more probability density functions (PDFs) is proposed for multimodal sensor processing. It approximates the unknown PDF by exponentially embedding the known PDFs. Such embedding is of a exponential family indexed by some parameters, and hence inherits many nice properties of the exponential family. It is shown that the approximated PDF is asymptotically the one that is the closest to the unknown PDF in Kullback-Leibler (KL) divergence. Applied to hypothesis testing, this approach shows improved performance compared to existing methods for cases of practical importance where the sensor outputs are not independent.

[1]  J. Pfanzagl,et al.  CONTRIBUTIONS TO A GENERAL ASYMPTOTIC STATISTICAL THEORY , 1982 .

[2]  David G. Luenberger,et al.  Linear and Nonlinear Programming: Second Edition , 2003 .

[3]  Lawrence D. Brown.  Fundamentals of Statistical Exponential Families , 1987 .

[4]  Ramanarayanan Viswanathan,et al.  Optimal distributed decision fusion , 1989 .

[5]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[6]  Pramod K. Varshney,et al.  Distributed detection of a nuclear radioactive source using fusion of correlated decisions , 2007, 2007 10th International Conference on Information Fusion.

[7]  Pramod K. Varshney,et al.  A parametric copula based framework for multimodal signal processing , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[8]  Steven Kay,et al.  Asymptotically Optimal Approximation of Multidimensional pdf's by Lower Dimensional pdf's , 2007, IEEE Transactions on Signal Processing.

[9]  S. Kay.  Exponentially embedded families - new approaches to model order estimation , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[10]  P.K. Varshney,et al.  Optimal Data Fusion in Multiple Sensor Detection Systems , 1986, IEEE Transactions on Aerospace and Electronic Systems.

[11]  James J. Higgins.  Some Surface Integral Techniques in Statistics , 1975 .

[12]  Carolyn Pillers Dobler,et al.  Mathematical Statistics , 2002 .

[13]  S. Kullback,et al.  Information Theory and Statistics , 1959 .

[14]  Albert H. Nuttall,et al.  Multidimensional probability density function approximations for detection, classification, and model order selection , 2001, IEEE Trans. Signal Process..

[15]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .