A Decentralized Approach for Nonlinear Prediction of Time Series Data in Sensor Networks

Wireless sensor networks rely on sensor devices deployed in an environment to support sensing and monitoring, including temperature, humidity, motion, and acoustic. Here, we propose a new approach to model physical phenomena and track their evolution by taking advantage of the recent developments of pattern recognition for nonlinear functional learning. These methods are, however, not suitable for distributed learning in sensor networks as the order of models scales linearly with the number of deployed sensors and measurements. In order to circumvent this drawback, we propose to design reduced order models by using an easy to compute sparsification criterion. We also propose a kernel-based least-mean-square algorithm for updating the model parameters using data collected by each sensor. The relevance of our approach is illustrated by two applications that consist of estimating a temperature distribution and tracking its evolution over time.

[1]  L. W. Jacobs,et al.  Note: A local-search heuristic for large set-covering problems , 1995 .

[2]  Ali H. Sayed,et al.  A Spatial Sampling Scheme Based on Innovations Diffusion in Sensor Networks , 2007, International Symposium on Information Processing in Sensor Networks.

[3]  Hichem Snoussi,et al.  Distributed Regression in Sensor Networks with a Reduced-Order Kernel Model , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[4]  Ralf Herbrich,et al.  Learning Kernel Classifiers: Theory and Algorithms , 2001 .

[5]  László Lovász,et al.  On the ratio of optimal integral and fractional covers , 1975, Discret. Math..

[6]  Christopher Taylor,et al.  Localization in Sensor Networks , 2005, Handbook of Sensor Networks.

[7]  Bernhard Schölkopf,et al.  A Generalized Representer Theorem , 2001, COLT/EuroCOLT.

[8]  Samuel Madden,et al.  Distributed regression: an efficient framework for modeling sensor network data , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[9]  Mung Chiang,et al.  The value of clustering in distributed estimation for sensor networks , 2005, 2005 International Conference on Wireless Networks, Communications and Mobile Computing.

[10]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[11]  Bruno Sinopoli,et al.  A kernel-based learning approach to ad hoc sensor network localization , 2005, TOSN.

[12]  Shie Mannor,et al.  The kernel recursive least-squares algorithm , 2004, IEEE Transactions on Signal Processing.

[13]  H. Vincent Poor,et al.  Distributed Kernel Regression: An Algorithm for Training Collaboratively , 2006, 2006 IEEE Information Theory Workshop - ITW '06 Punta del Este.

[14]  Francis J. Vasko,et al.  An efficient heuristic for large set covering problems , 1984 .

[15]  G. Wahba,et al.  Some results on Tchebycheffian spline functions , 1971 .

[16]  H. Vincent Poor,et al.  Distributed learning in wireless sensor networks , 2005, IEEE Signal Processing Magazine.

[17]  Konstantinos Psounis,et al.  Modeling spatially correlated data in sensor networks , 2006, TOSN.

[18]  Robert Nowak,et al.  Distributed optimization in sensor networks , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[19]  Cauligi S. Raghavendra,et al.  PEGASIS: Power-efficient gathering in sensor information systems , 2002, Proceedings, IEEE Aerospace Conference.

[20]  Anantha P. Chandrakasan,et al.  An application-specific protocol architecture for wireless microsensor networks , 2002, IEEE Trans. Wirel. Commun..

[21]  Ralf Herbrich,et al.  Learning Kernel Classifiers , 2001 .

[22]  Alfred O. Hero,et al.  Manifold learning algorithms for localization in wireless sensor networks , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[23]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[24]  J. Beasley,et al.  A genetic algorithm for the set covering problem , 1996 .

[25]  Paul Honeine,et al.  Online Prediction of Time Series Data With Kernels , 2009, IEEE Transactions on Signal Processing.

[26]  Alexander J. Smola,et al.  Online learning with kernels , 2001, IEEE Transactions on Signal Processing.

[27]  Michael I. Jordan,et al.  Nonparametric decentralized detection using kernel methods , 2005, IEEE Transactions on Signal Processing.

[28]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[29]  Paul Honeine,et al.  On-line Nonlinear Sparse Approximation of Functions , 2007, 2007 IEEE International Symposium on Information Theory.

[30]  G. Baudat,et al.  Kernel-based methods and function approximation , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[31]  M. Resende,et al.  A probabilistic heuristic for a computationally difficult set covering problem , 1989 .

[32]  Ian F. Akyildiz,et al.  Spatial correlation-based collaborative medium access control in wireless sensor networks , 2006, IEEE/ACM Transactions on Networking.

[33]  H. Vincent Poor,et al.  Regression in sensor networks: training distributively with alternating projections , 2005, SPIE Optics + Photonics.

[34]  Manfred Opper,et al.  Sparse Representation for Gaussian Process Models , 2000, NIPS.

[35]  Brian D. O. Anderson,et al.  Wireless sensor network localization techniques , 2007, Comput. Networks.

[36]  M. Aourid,et al.  Neural networks for the set covering problem: an application to the test vector compaction , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[37]  Deborah Estrin,et al.  Scalable, synthetic, sensor network data generation , 2005 .

[38]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[39]  Ali H. Sayed,et al.  Fundamentals Of Adaptive Filtering , 2003 .