published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

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During times of stock market turbulence and crises, monitoring the clustering behaviour of financial instruments allows one to better understand the behaviour of the stock market and the associated systemic risks. In the study undertaken, I apply an effective and performant approach to classify data clusters in order to better understand correlations between stocks. The novel methods aim to address the lack of effective algorithms to deal with high-performance cluster analysis in the context of large complex real-time low-latency data-sets. I apply an efficient and novel data clustering approach, namely the Giada and Marsili log-likelihood function derived from the Noh model and use a Parallel Genetic Algorithm in order to isolate residual data clusters. Genetic Algorithms (GAs) are a very versatile methodology for scientific computing, while the application of Parallel Genetic Algorithms (PGAs) further increases the computational efficiency. They are an effective vehicle to mine data sets for information and traits. However, the traditional parallel computing environment can be expensive. I focused on adopting NVIDIAs Compute Unified Device Architecture (CUDA) programming model in order to develop a PGA framework for my computation solution, where I aim to efficiently filter out residual clusters. The results show that the application of the PGA with the novel clustering function on the CUDA platform is quite effective to improve the computational efficiency of parallel data cluster analysis.

Ng Ka Ka. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 114-120). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.vii / Chapter I --- Projective Clustering --- p.1 / Chapter 1 --- Introduction to Projective Clustering --- p.2 / Chapter 2 --- Related Work to Projective Clustering --- p.7 / Chapter 2.1 --- CLARANS - Graph Abstraction and Bounded Optimization --- p.8 / Chapter 2.1.1 --- Graph Abstraction --- p.8 / Chapter 2.1.2 --- Bounded Optimized Random Search --- p.9 / Chapter 2.2 --- OptiGrid ´ؤ Grid Partitioning Approach and Density Estimation Function --- p.9 / Chapter 2.2.1 --- Empty Space Phenomenon --- p.10 / Chapter 2.2.2 --- Density Estimation Function --- p.11 / Chapter 2.2.3 --- Upper Bound Property --- p.12 / Chapter 2.3 --- CLIQUE and ENCLUS - Subspace Clustering --- p.13 / Chapter 2.3.1 --- Monotonicity Property of Subspaces --- p.14 / Chapter 2.4 --- PROCLUS Projective Clustering --- p.15 / Chapter 2.5 --- ORCLUS - Generalized Projective Clustering --- p.16 / Chapter 2.5.1 --- Singular Value Decomposition SVD --- p.17 / Chapter 2.6 --- "An ""Optimal"" Projective Clustering" --- p.17 / Chapter 3 --- EPC : Efficient Projective Clustering --- p.19 / Chapter 3.1 --- Motivation --- p.19 / Chapter 3.2 --- Notations and Definitions --- p.21 / Chapter 3.2.1 --- Density Estimation Function --- p.22 / Chapter 3.2.2 --- 1-d Histogram --- p.23 / Chapter 3.2.3 --- 1-d Dense Region --- p.25 / Chapter 3.2.4 --- Signature Q --- p.26 / Chapter 3.3 --- The overall framework --- p.28 / Chapter 3.4 --- Major Steps --- p.30 / Chapter 3.4.1 --- Histogram Generation --- p.30 / Chapter 3.4.2 --- Adaptive discovery of dense regions --- p.31 / Chapter 3.4.3 --- Count the occurrences of signatures --- p.36 / Chapter 3.4.4 --- Find the most frequent signatures --- p.36 / Chapter 3.4.5 --- Refine the top 3m signatures --- p.37 / Chapter 3.5 --- Time and Space Complexity --- p.38 / Chapter 4 --- EPCH: An extension and generalization of EPC --- p.40 / Chapter 4.1 --- Motivation of the extension --- p.40 / Chapter 4.2 --- Distinguish clusters by their projections in different subspaces --- p.43 / Chapter 4.3 --- EPCH: a generalization of EPC by building histogram with higher dimensionality --- p.46 / Chapter 4.3.1 --- Multidimensional histograms construction and dense re- gions detection --- p.46 / Chapter 4.3.2 --- Compressing data objects to signatures --- p.47 / Chapter 4.3.3 --- Merging Similar Signature Entries --- p.49 / Chapter 4.3.4 --- Associating membership degree --- p.51 / Chapter 4.3.5 --- The choice of Dimensionality d of the Histogram --- p.52 / Chapter 4.4 --- Implementation of EPC2 --- p.53 / Chapter 4.5 --- Time and Space Complexity of EPCH --- p.54 / Chapter 5 --- Experimental Results --- p.56 / Chapter 5.1 --- Clustering Quality Measurement --- p.56 / Chapter 5.2 --- Synthetic Data Generation --- p.58 / Chapter 5.3 --- Experimental setup --- p.59 / Chapter 5.4 --- Comparison between EPC and PROCULS --- p.60 / Chapter 5.5 --- Comparison between EPCH and ORCLUS --- p.62 / Chapter 5.5.1 --- Dimensionality of the original space and the associated subspace --- p.65 / Chapter 5.5.2 --- Projection not parallel to original axes --- p.66 / Chapter 5.5.3 --- Data objects belong to more than one cluster under fuzzy clustering --- p.67 / Chapter 5.6 --- Scalability of EPC --- p.68 / Chapter 5.7 --- Scalability of EPC2 --- p.69 / Chapter 6 --- Conclusion --- p.71 / Chapter II --- Multiple Tables Association Rules Mining --- p.74 / Chapter 7 --- Introduction to Multiple Tables Association Rule Mining --- p.75 / Chapter 7.1 --- Problem Statement --- p.77 / Chapter 8 --- Related Work to Multiple Tables Association Rules Mining --- p.80 / Chapter 8.1 --- Aprori - A Bottom-up approach to generate candidate sets --- p.80 / Chapter 8.2 --- VIPER - Vertical Mining with various optimization techniques --- p.81 / Chapter 8.2.1 --- Vertical TID Representation and Mining --- p.82 / Chapter 8.2.2 --- FORC --- p.83 / Chapter 8.3 --- Frequent Itemset Counting across Multiple Tables --- p.84 / Chapter 9 --- The Proposed Method --- p.85 / Chapter 9.1 --- Notations --- p.85 / Chapter 9.2 --- Converting Dimension Tables to internal representation --- p.87 / Chapter 9.3 --- The idea of discovering frequent itemsets without joining --- p.89 / Chapter 9.4 --- Overall Steps --- p.91 / Chapter 9.5 --- Binding multiple Dimension Tables --- p.92 / Chapter 9.6 --- Prefix Tree for FT --- p.94 / Chapter 9.7 --- Maintaining frequent itemsets in FI-trees --- p.96 / Chapter 9.8 --- Frequency Counting --- p.99 / Chapter 10 --- Experiments --- p.102 / Chapter 10.1 --- Synthetic Data Generation --- p.102 / Chapter 10.2 --- Experimental Findings --- p.106 / Chapter 11 --- Conclusion and Future Works --- p.112 / Bibliography --- p.114

Lau Hei Yuet. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 74-76). / Abstracts in English and Chinese. / Abstract --- p.i / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Cluster Analysis --- p.1 / Chapter 1.2 --- Dissimilarity Measures --- p.3 / Chapter 1.2.1 --- Continuous Data --- p.4 / Chapter 1.2.2 --- Categorical and Nominal Data --- p.4 / Chapter 1.2.3 --- Mixed Data --- p.5 / Chapter 1.2.4 --- Missing Data --- p.6 / Chapter 1.3 --- Outline of the thesis --- p.6 / Chapter 2 --- Clustering Algorithms --- p.9 / Chapter 2.1 --- The k-means Algorithm Family --- p.9 / Chapter 2.1.1 --- The Algorithms --- p.9 / Chapter 2.1.2 --- Choosing the Number of Clusters - the MaxMin Algo- rithm --- p.12 / Chapter 2.1.3 --- Starting Configuration - the MaxMin Algorithm --- p.16 / Chapter 2.2 --- Clustering Using Unidimensional Scaling --- p.16 / Chapter 2.2.1 --- Unidimensional Scaling --- p.16 / Chapter 2.2.2 --- Procedures --- p.17 / Chapter 2.2.3 --- Guttman's Updating Algorithm --- p.18 / Chapter 2.2.4 --- Pliner's Smoothing Algorithm --- p.18 / Chapter 2.2.5 --- Starting Configuration --- p.19 / Chapter 2.2.6 --- Choosing the Number of Clusters --- p.21 / Chapter 2.3 --- Cluster Validation --- p.23 / Chapter 2.3.1 --- Continuous Data --- p.23 / Chapter 2.3.2 --- Nominal Data --- p.24 / Chapter 2.3.3 --- Resampling Method --- p.25 / Chapter 2.4 --- Conclusion --- p.27 / Chapter 3 --- Experimental Results --- p.29 / Chapter 3.1 --- Simulated Data 1 --- p.29 / Chapter 3.2 --- Simulated Data 2 --- p.35 / Chapter 3.3 --- Iris Data --- p.41 / Chapter 3.4 --- Wine Data --- p.47 / Chapter 3.5 --- Mushroom Data --- p.53 / Chapter 3.6 --- Conclusion --- p.59 / Chapter 4 --- Large Database --- p.61 / Chapter 4.1 --- Sliding Windows Algorithm --- p.61 / Chapter 4.2 --- Two-stage Algorithm --- p.63 / Chapter 4.3 --- Three-stage Algorithm --- p.65 / Chapter 4.4 --- Experimental Results --- p.66 / Chapter 4.5 --- Conclusion --- p.68 / Chapter A --- Algorithms --- p.69 / Chapter A.1 --- MaxMin Algorithm --- p.69 / Chapter A.2 --- Sliding Windows Algorithm --- p.70 / Chapter A.3 --- Two-stage Algorithm - Stage One --- p.72 / Chapter A.4 --- Two-stage Algorithm - Stage Two --- p.73 / Bibliography --- p.74

Chu Pok Nang. / Thesis submitted on: October 2002. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 69-73). / Abstracts in English and Chinese. / Chapter 1. --- Introduction / Group Technology --- p.6 / Purposes of Research --- p.10 / The Outline of this Thesis --- p.13 / Chapter 2. --- Literature Review / Algorithms for Group Technology --- p.14 / Hierarchical Clustering Approaches --- p.17 / Sorting Based Approaches --- p.18 / Heuristic Exchange Approaches --- p.19 / Seed Based Approaches --- p.20 / Simulated Annealing Approaches --- p.20 / Tabu Search Approaches --- p.21 / Genetic Algorithm Approaches --- p.21 / Neural Network Approaches --- p.22 / Cluster Identification Approaches --- p.22 / Chapter 3. --- The Group Technology Problem / Representing a Manufacturing System --- p.25 / Machine-Part Incidence Matrix --- p.26 / Chapter 4. --- The Improved Cluster Identification Algorithm / Cluster Identification --- p.34 / Formulation --- p.35 / Branch-and-Bound Method --- p.37 / Original Cluster Identification Algorithm --- p.39 / Branching Rule --- p.44 / Chapter 5. --- Computational Studies / Plans for Comparative Studies --- p.49 / Comparison with Existing Cluster Identification Approaches --- p.51 / Solutions to Some Well-known Problems --- p.53 / Comparison with an Optimal Method --- p.60 / Chapter 6. --- Conclusion --- p.63 / Reference --- p.69

The purpose of this study is to analyze consumer behavior in bride cake market. The study divides into two parts: one aims consumers who married before 1996 and are above 40-year-old. Through deep interviewing, we can profile consumer behavior in the bribe cake before 1996. The sample of the second study is singles of 18 to 35 years old. According to decision process of EKB model, this research tries to realize consumer purchasing behavior. The results of this research are as follows: 1. The scale of bride cake industry won¡¦t diminish at the present time. 2. Acceptable price is rising up. 3. Western bride cake is consumer¡¦s favorite, then goes to the mixed form. 4. Famous bride cake chain store is the most favorite buying place. 5. Credit is the favorite payment pattern. 6. Valuable information comes from relatives, friends, and store¡¦s sales. 7. In terms of product attributes, consumer emphasizes ¡§good taste¡¨, ¡§good services¡¨, and ¡§fair price¡¨. 8. Geographical variables don¡¦t have significant differences in consumer behavior. 9. Via cluster analysis, samples are divided into three groups, namely ¡§Fashion Seeker¡¨, ¡§Innovator and Adventurer¡¨, and ¡§Realist and economist¡¨. In terms of demographic variables, significant differences exist only in sex and age. There are more female in ¡§Fashion Seeker¡¨ and ¡§Realist and economist¡¨. And the age in these two groups is for the most part range from 18 to 25 years old. The age of ¡§Innovator and Adventurer¡¨ is for the most part range from 26 to 30 years old. ¡§Fashion Seeker¡¨ values ¡§vogue¡¨, ¡§beautiful looking¡¨ and ¡§notable brand¡¨, and concerned ¡§TV advertisement¡¨.

Thesis (Ph. D.)--University of Cincinnati, 2006. / Includes bibliographical references (leaf 142-147). Also available online.

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Statistics and Biostatistics." Includes bibliographical references (p. 75-78).