GeoEntropy: A measure of complexity and similarity

Measuring the complexity of a pattern expressed either in time or space has been introduced to quantify the information content of the pattern, which can then be applied for classification. Such information measures are particularly useful for the understanding of systems complexity in many fields of sciences, business and engineering. The novel concept of geostatistical entropy (GeoEntropy) as a measure of pattern complexity and similarity is addressed in this paper. It has been experimentally shown that GeoEntropy is an effective algorithm for studying signal predictability and has superior capability of classifying complex bio-patterns.

[1]  Ki H. Chon,et al.  Automatic Selection of the Threshold Value $r$ for Approximate Entropy , 2008, IEEE Transactions on Biomedical Engineering.

[2]  C. Peng,et al.  What is physiologic complexity and how does it change with aging and disease? , 2002, Neurobiology of Aging.

[3]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[4]  Tuan D. Pham,et al.  A probabilistic measure for alignment-free sequence comparison , 2004, Bioinform..

[5]  Madalena Costa,et al.  Multiscale entropy analysis of complex physiologic time series. , 2002, Physical review letters.

[6]  I. Cosic.  Macromolecular bioactivity: is it resonant interaction between macromolecules?-theory and applications , 1994, IEEE Transactions on Biomedical Engineering.

[7]  Jeffrey M. Hausdorff,et al.  Fractal dynamics in physiology: Alterations with disease and aging , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Claudio Cobelli,et al.  Ovarian cancer identification based on dimensionality reduction for high-throughput mass spectrometry data , 2005, Bioinform..

[9]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[10]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[11]  Madalena Costa,et al.  Multiscale entropy analysis of biological signals. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  R. Reyment,et al.  Statistics and Data Analysis in Geology. , 1988 .

[13]  Xiaobo Zhou,et al.  Classification of Mass Spectrometry Based Protein Markers by Kriging Error Matching , 2008, MDA.

[14]  Webb Miller,et al.  Comparison of genomic DNA sequences: solved and unsolved problems , 2001, Bioinform..

[15]  S. Pincus.  Approximate entropy (ApEn) as a complexity measure. , 1995, Chaos.

[16]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[17]  Qiang Fang,et al.  Protein sequence comparison based on the wavelet transform approach. , 2002, Protein engineering.

[18]  M. Stein.  Estimating and choosing , 1989 .

[19]  D. Krane,et al.  Fundamental Concepts of Bioinformatics , 2002 .

[20]  A L Goldberger,et al.  Physiological time-series analysis: what does regularity quantify? , 1994, The American journal of physiology.

[21]  Jan Khre,et al.  The Mathematical Theory of Information , 2012 .

[22]  A. L. Short,et al.  Sample entropy of electrocardiographic RR and QT time-series data during rest and exercise , 2007, Physiological measurement.

[23]  Michael Edward Hohn,et al.  An Introduction to Applied Geostatistics: by Edward H. Isaaks and R. Mohan Srivastava, 1989, Oxford University Press, New York, 561 p., ISBN 0-19-505012-6, ISBN 0-19-505013-4 (paperback), $55.00 cloth, $35.00 paper (US) , 1991 .

[24]  David Applebaum.  Probability and information , 1996 .

[25]  Peter Grassberger,et al.  Entropy estimation of symbol sequences. , 1996, Chaos.

[26]  A. Vlahou,et al.  Proteomic approaches to biomarker discovery in prostate and bladder cancers , 2001, Proteomics.

[27]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.