Abstract
An information-statistical approach is proposed for analyzing temporal-spatial data. The basic idea is to analyze the temporal aspect of the data by first conditioning on specific spatial nature of the data. Parametric approach based on Guassian model is employed for analyzing the temporal behavior of the data. Schwarz information criterion is then applied to detect multiple mean change points --- thus the Gaussian statistical models - to account for changes of the population mean over time. To examine the spatial characteristics of the data, successive mean change points are qualified by finite categorical values. The distribution of the finite categorical values is then used to estimate a non-parametric probability model through a non-linear SVD-based optimization approach; where the optimization criterion is Shannon expected entropy. This optimal probability model accounts for the spatial characteristics of the data and is then used to derive spatial association patterns subject to chi-square statistic hypothesis test.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Fayyad, U.M. and Piatetsky-Shapiro, G. and Smyth, P.: From Data Mining to Knowledge Discovery: An Overview, in Advances in Knowledge Discovery and Data Mining, (editors: Fayyad, U. M. and Piatetsky-Shapiro, G. and Smyth, P. and Uthurusamy, R.). AAAI Press / MIT Press, (1996) Chapter 1, 1–34.
Jumarie, G., Relative Information: Theory and Applications, Springer-Verlag (1990).
Nyquist H., Certain Topics in Telegraph Transmission Theory, A.I.E.E. Transaction, V. 47, April (1928).
Shannon, C.E. and Weaver, W., The Mathematical Theory of Communication, University of Urbana Press, Urbana (1972).
Kullback S., Information and Statistics, Wiley and Sons, NY (1959).
Good I.J., Weight of Evidence, “Correlation, Explanatory Power, Information, and the Utility of Experiments,” Journal of Royal Statistics Society, Ser. B, 22, (1960) 319–331.
Goodman L.A., “The analysis of cross-classified data: Independence, quasi-independence and interactions in contingency tables with and without missing entries,” Journal of the American Statistical Association, 63:1091–1131 (1968).
Grenander U., Pattern Analysis: LecturesinPatternTheory: V2, Applied Mathematical Sciences 24, Springer-Verlag, ISBN 0-387-90310-0 (1978).
Grenander U., Chow Y. Keenan K.M., HANDS: A Pattern Theoretic Study of Biological Shapes, Springer-Verlag, New York (1991).
Grenander U., General Pattern Theory, Oxford University Press (1993).
Grenander U., Elements of Pattern Theory, The Johns Hopkins University Press, ISBN 0-8018-5187-4 (1996).
Kullback S. and Leibler R., “On Information and Sufficiency,” Ann. Math. Statistics, 22 (1951) 79-86.
Kullback S., Information and Statistics, Wiley and Sons, NY, (1959).
Haberman S.J. “TheAnalysisof Residuals inCross-classifiedTables,” Biometrics, 29 (1973) 205–220.
Cover T.M. and Thomas J.A., Elements of Information Theory, Wiley (1991).
Chen J. and Gupta A.K., “Information Criterion and Change Point Problem for Regular Models,” Technical Report No. 98-05, Department of Mathematics and Statistics., Bowling Green State U.,Ohio (1998).
Vostrikova L. Ju., “Detecting disorder in multidimensional random process,” Soviet Math. Dokl., 24, 55–59, (1981).
Schwarz G., “Estimating the dimension of a model,” Ann. Statist., 6, 461–464 (1978).
Gupta, A.K. and Chen, J., “Detecting Changes of mean in Multidimensional Normal Sequences with Applications to Literature and Geology,” Computational Statistics, 11:211–221, 1996, Physica-Verlag, Heidelberg (1996).
Wright S., Primal-Dual Interior-Point Methods, SIAM, ISBN 0-89871-382-X (1997).
Sy B.K., “Probability Model Selection Using Information-Theoretic Optimization Criterion,” Journal of Statistical Computing and Simulation, Gordon and Breach Publishing Group, NJ, 69(3), (2001).
Fisher R.A., “The conditions under which χ2 measures the discrepancy between observation and hypothesis,” Journal of the Royal Statistical Society, 87 (1924) 442–450.
Wong A.K.C. and Wang Y., “High Order Pattern Discovery from Discrete-valued Data,” IEEE Trans. On Knowledge and Data Engineering, 9(6), (1997) 877–893.
www http://bonnet2.cs.qc.edu:1099/data_warehouse/plsql/rd_start.main
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sy, B.K., Gupta, A.K. (2001). Data Mining Approach Based on Information-Statistical Analysis: Application to Temporal-Spatial Data. In: Perner, P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2001. Lecture Notes in Computer Science(), vol 2123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44596-X_11
Download citation
DOI: https://doi.org/10.1007/3-540-44596-X_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42359-1
Online ISBN: 978-3-540-44596-8
eBook Packages: Springer Book Archive