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Entropy-based subspace clustering for mining numerical data.

by Cheng, Chun-hung.Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.Includes bibliographical references (leaves 72-76).Abstracts in English and Chinese.Abstract --- p.iiAcknowledgments --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Six Tasks of Data Mining --- p.1Chapter 1.1.1 --- Classification --- p.2Chapter 1.1.2 --- Estimation --- p.2Chapter 1.1.3 --- Prediction --- p.2Chapter 1.1.4 --- Market Basket Analysis --- p.3Chapter 1.1.5 --- Clustering --- p.3Chapter 1.1.6 --- Description --- p.3Chapter 1.2 --- Problem Description --- p.4Chapter 1.3 --- Motivation --- p.5Chapter 1.4 --- Terminology --- p.7Chapter 1.5 --- Outline of the Thesis --- p.7Chapter 2 --- Survey on Previous Work --- p.8Chapter 2.1 --- Data Mining --- p.8Chapter 2.1.1 --- Association Rules and its Variations --- p.9Chapter 2.1.2 --- Rules Containing Numerical Attributes --- p.15Chapter 2.2 --- Clustering --- p.17Chapter 2.2.1 --- The CLIQUE Algorithm --- p.20Chapter 3 --- Entropy and Subspace Clustering --- p.24Chapter 3.1 --- Criteria of Subspace Clustering --- p.24Chapter 3.1.1 --- Criterion of High Density --- p.25Chapter 3.1.2 --- Correlation of Dimensions --- p.25Chapter 3.2 --- Entropy in a Numerical Database --- p.27Chapter 3.2.1 --- Calculation of Entropy --- p.27Chapter 3.3 --- Entropy and the Clustering Criteria --- p.29Chapter 3.3.1 --- Entropy and the Coverage Criterion --- p.29Chapter 3.3.2 --- Entropy and the Density Criterion --- p.31Chapter 3.3.3 --- Entropy and Dimensional Correlation --- p.33Chapter 4 --- The ENCLUS Algorithms --- p.35Chapter 4.1 --- Framework of the Algorithms --- p.35Chapter 4.2 --- Closure Properties --- p.37Chapter 4.3 --- Complexity Analysis --- p.39Chapter 4.4 --- Mining Significant Subspaces --- p.40Chapter 4.5 --- Mining Interesting Subspaces --- p.42Chapter 4.6 --- Example --- p.44Chapter 5 --- Experiments --- p.49Chapter 5.1 --- Synthetic Data --- p.49Chapter 5.1.1 --- Data Generation ´ؤ Hyper-rectangular Data --- p.49Chapter 5.1.2 --- Data Generation ´ؤ Linearly Dependent Data --- p.50Chapter 5.1.3 --- Effect of Changing the Thresholds --- p.51Chapter 5.1.4 --- Effectiveness of the Pruning Strategies --- p.53Chapter 5.1.5 --- Scalability Test --- p.53Chapter 5.1.6 --- Accuracy --- p.55Chapter 5.2 --- Real-life Data --- p.55Chapter 5.2.1 --- Census Data --- p.55Chapter 5.2.2 --- Stock Data --- p.56Chapter 5.3 --- Comparison with CLIQUE --- p.58Chapter 5.3.1 --- Subspaces with Uniform Projections --- p.60Chapter 5.4 --- Problems with Hyper-rectangular Data --- p.62Chapter 6 --- Miscellaneous Enhancements --- p.64Chapter 6.1 --- Extra Pruning --- p.64Chapter 6.2 --- Multi-resolution Approach --- p.65Chapter 6.3 --- Multi-threshold Approach --- p.68Chapter 7 --- Conclusion --- p.70Bibliography --- p.71Appendix --- p.77Chapter A --- Differential Entropy vs Discrete Entropy --- p.77Chapter A.1 --- Relation of Differential Entropy to Discrete Entropy --- p.78Chapter B --- Mining Quantitative Association Rules --- p.80Chapter B.1 --- Approaches --- p.81Chapter B.2 --- Performance --- p.82Chapter B.3 --- Final Remarks --- p.8