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Minimum Cross-Entropy Approximation for Modeling of Highly Intertwining Data Sets at Subclass Levels

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Abstract

We study the problem of how to accurately model the data sets that contain a number of highly intertwining sets in terms of their spatial distributions. Applying the Minimum Cross-Entropy minimization technique, the data sets are placed into a minimum number of subclass clusters according to their high intraclass and low interclass similarities. The method leads to a derivation of the probability density functions for the data sets at the subclass levels. These functions then, in combination, serve as an approximation to the underlying functions that describe the statistical features of each data set.

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References

  • Avi-Itzhak, H.I., Van Mieghem, J.A., and Rub, L. (1995). Multiple Subclass Pattern Recognition: A Maximin Correlation Approach, IEEE Trans. Pattern Anal., Machine Intell., 17(4), 418-431.

    Google Scholar 

  • Banfield, J.D. and Raftery, A.E. (1993). Model-Based Gaussian and Non-Gaussian Clustering, Biometrics, 49, 803-821.

    Google Scholar 

  • Bennett, K.P. and Mangasarian, O.L. (1992). Robust Linear Programming Discrimination of Two Linearly Inseparable Sets, Optimization Methods and Software, 1, 23-34.

    Google Scholar 

  • Chan, K.P. and Cheung, Y.S. (1992). Clustering of Clusters, Pattern Recognition, 25(2), 211-217.

    Google Scholar 

  • Duda, R.O. and Hart, P.E. (1973). Pattern Classification and Scene Analysis, John Wiley & Sons.

  • Ishibuchi, H., Nozaki, H.K., and Tanaka, H. (1993). Efficient Fuzzy Partition of Pattern Space for Classification Problems, Fuzzy Sets and Systems, 59, 295-304.

    Google Scholar 

  • Jones, L.K. and Byrne, C.L. (1990). General Entropy Criteria for Inverse Problems, with Applications to Data Compression, Pattern Classification, and Cluster Analysis, IEEE Transactions on Information Theory, 36(1), 23-30.

    Google Scholar 

  • Juang, B.H. and Katagiri, S. (1992). Discriminative Learning for Minimum Error Classification, IEEE Transactions on Signal Processing, 40, 3043-3054.

    Google Scholar 

  • Man, Y. and Gath, I. (1994). Detection and Separation of Ring-Shaped Clusters using Fuzzy Clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(8), 855-861.

    Google Scholar 

  • Nath, R., Jackson, W., and Jones, T.W. (1992). A Comparison of the Classical and the Linear Programming Approaches to the Classification Problem in Discriminant Analysis, Journal of Statistical Computation and Simulation, 41(1), 73-93.

    Google Scholar 

  • Ney, H. (1995). On the Probablistic Interpretation of Neural Network Classifiers and Discriminative Training Criteria, IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(2), 107-119.

    Google Scholar 

  • Rao, C.R. and Nayak, T.K. (1985). Cross-Entropy, Dissimilarity Measures, and Characterizations of Quadratic Entropy, IEEE Transactions on Information Theory, 31(5).

  • Shore, J.E. and Gray, R.M. (1982). Minimum Cross-Entropy Pattern Classification and Cluster Analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(1), 11-17.

    Google Scholar 

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Zhu, Q. Minimum Cross-Entropy Approximation for Modeling of Highly Intertwining Data Sets at Subclass Levels. Journal of Intelligent Information Systems 11, 139–152 (1998). https://doi.org/10.1023/A:1008680819565

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