PROFHMM_UNC: Introducing a Priori Knowledge for Completing Missing Values of Multidimensional Time-Series

A. A.  Charantonis; F.  Badran; S.  Thiria

doi:10.4236/ijcns.2014.78034

A. A. Charantonis, F. Badran, S. Thiria

Abstract: We present a new method for estimating missing values or correcting unreliable observed values of time dependent physical fields. This method, is based on Hidden Markov Models and Self-Organizing Maps, and is named PROFHMM_UNC. PROFHMM_UNC combines the knowledge of the physical process under study provided by an already known dynamic model and the truncated time series of observations of the phenomenon. In order to generate the states of the Hidden Markov Model, Self-Organizing Maps are used to discretize the available data. We make a modification to the Viterbi algorithm that forces the algorithm to take into account a priori information on the quality of the observed data when selecting the optimum reconstruction. The validity of PROFHMM_UNC was endorsed by performing a twin experiment with the outputs of the ocean biogeochemical NEMO-PISCES model.

Keywords: Multidimensional Time-Series Completion, Hidden Markov Models, Self-Organizing Maps

Cite this paper: Charantonis, A. , Badran, F. and Thiria, S. (2014) PROFHMM_UNC: Introducing a Priori Knowledge for Completing Missing Values of Multidimensional Time-Series. International Journal of Communications, Network and System Sciences, 7, 316-329. doi: 10.4236/ijcns.2014.78034.

References

[1] Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977) Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B, 39, 1-38.

[2] Ghahramani, Z. and Jordan, M.I. (1994) Supervised Learning from Incomplete Data via an EM Approach. Advances in Neural Information Processing Systems (NIPS 6), Morgan Kauffman, San Fransisco, 120-127.

[3] Wasito, I. and Mirkin, B. (2005) Nearest Neighbour Approach in the Least-Squares Data Imputation Algorithms. Information Sciences, 169, 1-25.

[4] Chiewchanwattana, S., Lursinsap, C. and Chu, C.-H.H. (2007) Imputing Incomplete Time-Series Data Based on Varied-Window Similarity Measure of Data Sequences. Pattern Recognition Letters, 28, 1091-1103. http://dx.doi.org/10.1016/j.patrec.2007.01.008

[5] Prasomphan, S., Lursinsap, C. and Chiewchanwattana, S. (2009) Imputing Time Series Data by Regional-Gradient-Guided Bootstrapping Algorithm. Proceedings of the 9th International Symposium on Communications and Information Technology, Incheon, 163-168.

[6] Grayzeck, E. (2011) National Space Science Data Center, Archive Plan for 2010-2013. NSSDC Archive Plan 10-13.

[7] Robinson, A.R. and Lermusiaux, P.F.J. (2000) Overview of Data Assimilation. Harvard Reports in Physical/Interdisciplinary, Ocean Science, No. 62.

[8] Viterbi, A.J. (1967) Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding
Algorithm. IEEE Transactions on Information Theory, 13, 260-269. http://dx.doi.org/10.1109/TIT.196
7.1054010

[9] Charantonis, A.A., Brajard, J., Moulin, C., Bardan, F. and Thiria, S. (2011) Inverse Method for the Retrieval of Ocean Vertical Profiles Using Self Organizing Maps and Hidden Markov Models—Application on Ocean Colour Satellite Image Inversion. IJCCI (NCTA), 316-321.

[10] Jaziri, R., Lebbah, M., Bennani, Y. and Chenot, J-H. (2011) SOS-HMM: Self-Organizing Structure of Hidden Markov Model, Artificial Neural Networks and Machine Learning—ICANN 2011. Lecture Notes in Computer Science, 6792, 87-94. http://dx.doi.org/10.1007/978-3-642-21738-8_12

[11] Madec, G. (2008) NEMO Ocean Engine. Note du Pole de modélisation, Institut Pierre-Simon Laplace (IPSL), France.

[12] Willsky, A.S. (2002) Multiresolution Markov Models for Signal and Image Processing. Proceedings of the IEEE, 90, 1396-1458. http://dx.doi.org/10.1109/JPROC.2002.800717

[13] Jolliffe, I.T. (2002) Principal Component Analysis. 2nd Edition, Springer, Berlin.

[14] Kwan, C., Zhang, X., Xu, R. and Haynes, L. (2003) A Novel Approach to Fault Diagnostics and Prognostics. Proceedings of the 2003 IEEE International Conference Robotics & Automation, Taipei.

[15] Kohonen, T. (1990) The Self-Organizing Map. Proceedings of the IEEE, 78.
http://www.cis.hut.fi/projects/somtoolbox/package/docs2/somtoolbox.html

[16] Doneya, S.C., Kleypasa, J.A., Sarmientob, J.L. and Falkowski, P.G. (2002) The US JGOFS Synthesis and Modeling Project—An Introduction. Deep-Sea Research II, 49, 1-20.
http://dx.doi.org/10.1016/S0967-0645(01)00092-3

[17] Viterbi, A.J. (1998) An Intuitive Justification and a Simplified Implementation of a MAP Decoder for Convolutional Codes. IEEE Journal on Selected Areas in Communications, 16, 260-264.
http://dx.doi.org/10.1109/49.661114

[18] Hagenauer, J. and Hoeher, P. (1989) A Viterbi Algorithm with Soft-Decision Outputs and Its Applications. IEEE Global Telecommunications Conference and Exhibition “Communications Technology for the 1990s and Beyond” (GLOBECOM), 1680-1686.