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The mitigation of outliers serves to increase the strength of a relationship between variables. This study defined outliers in three different ways and used five regression procedures to describe the effects of outliers on 50 data sets. This study also examined the relationship among the shape of the distribution, skewness, and outliers.

Tse Suk Yan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 114-115). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- The Elements of the New Procedure --- p.6 / Chapter 2.1 --- The Stepping Algorithm --- p.6 / Chapter 2.2 --- Outlier Measure and Benchmark --- p.17 / Chapter Chapter 3 --- The New Procedure --- p.21 / Chapter 3.1 --- Procedure --- p.22 / Chapter 3.2 --- Examples --- p.31 / Chapter 3.3 --- Simulation Study --- p.41 / Chapter 3.3.1 --- Terms and Factors --- p.41 / Chapter 3.3.2 --- Procedure --- p.45 / Chapter 3.3.3 --- Results --- p.47 / Chapter Chapter 4 --- Robust Version of the New Procedure --- p.51 / Chapter 4.1 --- Procedure --- p.52 / Chapter 4.2 --- Examples --- p.58 / Chapter 4.3 --- Simulation Study --- p.62 / Chapter 4.3.1 --- Procedure --- p.63 / Chapter 4.3.2 --- Results --- p.65 / Chapter Chapter 5 --- The New Procedure with Random Initial Subset --- p.68 / Chapter 5.1 --- The Elements --- p.69 / Chapter 5.2 --- Procedure --- p.71 / Chapter 5.3 --- Examples --- p.77 / Chapter Chapter 6 --- Discussion --- p.91 / Chapter Chapter 7 --- Conclusion --- p.102 / Appendix --- p.105 / References --- p.114

Ng Sau-chun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 53-54). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- The Local Influence Approach --- p.5 / Chapter 2.1 --- Review of the local influence approach / Chapter 2.2 --- Recent modification of the approach / Chapter Chapter 3 --- Detection of Outliers --- p.9 / Chapter 3.1 --- A measure to identify multivariate outliers / Chapter 3.2 --- Identification of outliers in the presence of ordinal categorical variables / Chapter 3.3 --- Examples / Chapter 3.3.1 --- Example --- p.1 / Chapter 3.3.2 --- Example --- p.2 / Chapter 3.3.3 --- Example --- p.3 / Chapter 3.4 --- Behavior of the measure under different patterns / Chapter 3.5 --- Outlying observations and their influence on the estimate of polychoric correlation / Chapter 3.5.1 --- Example / Chapter 3.5.2 --- The simulation studies / Chapter Chapter 4 --- Influential Cells in A Contingency Table --- p.28 / Chapter 4.1 --- The model and its estimation / Chapter 4.2 --- The perturbation of observed frequency / Chapter 4.3 --- Normal curvatures as an influence measures / Chapter 4.4 --- Some numerical results / Chapter 4.4.1 --- 2-Dimensional data examples / Chapter 4.4.2 --- Examples on m-Dimensional data / Chapter Chapter 5 --- Discussion --- p.51 / Bibliography / Appendix

Typescript (photocopy). / Digitized by Kansas Correctional Industries

by Terry Shing-fong Lew. / "July 1999." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (p. 52-54). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Chiu Lai Mei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 142-149). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.vi / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Outlier Analysis --- p.2 / Chapter 1.2 --- Problem Statement --- p.4 / Chapter 1.2.1 --- Binary Property of Outlier --- p.4 / Chapter 1.2.2 --- Overlapping Clusters with Different Densities --- p.4 / Chapter 1.2.3 --- Large Datasets --- p.5 / Chapter 1.2.4 --- High Dimensional Datasets --- p.6 / Chapter 1.3 --- Contributions --- p.8 / Chapter 2 --- Related Work in Outlier Detection --- p.10 / Chapter 2.1 --- Outlier Detection --- p.11 / Chapter 2.1.1 --- Clustering-Based Methods --- p.11 / Chapter 2.1.2 --- Distance-Based Methods --- p.14 / Chapter 2.1.3 --- Density-Based Methods --- p.18 / Chapter 2.1.4 --- Deviation-Based Methods --- p.22 / Chapter 2.2 --- Breakthrough Outlier Notion: Degree of Outlier-ness --- p.25 / Chapter 2.2.1 --- LOF: Local Outlier Factor --- p.26 / Chapter 2.2.2 --- Definitions --- p.26 / Chapter 2.2.3 --- Properties --- p.29 / Chapter 2.2.4 --- Algorithm --- p.30 / Chapter 2.2.5 --- Time Complexity --- p.31 / Chapter 2.2.6 --- LOF of High Dimensional Data --- p.31 / Chapter 3 --- LOF': Formula with Intuitive Meaning --- p.33 / Chapter 3.1 --- Definition of LOF' --- p.33 / Chapter 3.2 --- Properties --- p.34 / Chapter 3.3 --- Time Complexity --- p.37 / Chapter 4 --- "LOF"" for Detecting Small Groups of Outliers" --- p.39 / Chapter 4.1 --- "Definition of LOF"" " --- p.40 / Chapter 4.2 --- Properties --- p.41 / Chapter 4.3 --- Time Complexity --- p.44 / Chapter 5 --- GridLOF for Pruning Reasonable Portions from Datasets --- p.46 / Chapter 5.1 --- GridLOF Algorithm --- p.47 / Chapter 5.2 --- Determine Values of Input Parameters --- p.51 / Chapter 5.2.1 --- Number of Intervals w --- p.51 / Chapter 5.2.2 --- Threshold Value σ --- p.52 / Chapter 5.3 --- Advantages --- p.53 / Chapter 5.4 --- Time Complexity --- p.55 / Chapter 6 --- SOF: Efficient Outlier Detection for High Dimensional Data --- p.57 / Chapter 6.1 --- Motivation --- p.57 / Chapter 6.2 --- Notations and Definitions --- p.59 / Chapter 6.3 --- SOF: Subspace Outlier Factor --- p.62 / Chapter 6.3.1 --- Formal Definition of SOF --- p.62 / Chapter 6.3.2 --- Properties of SOF --- p.67 / Chapter 6.4 --- SOF-Algorithm: the Overall Framework --- p.73 / Chapter 6.5 --- Identify Associated Subspaces of Clusters in SOF-Algorithm . . --- p.74 / Chapter 6.5.1 --- Technical Details in Phase I --- p.76 / Chapter 6.6 --- Technical Details in Phase II and Phase III --- p.88 / Chapter 6.6.1 --- Identify Outliers --- p.88 / Chapter 6.6.2 --- Subspace Quantization --- p.90 / Chapter 6.6.3 --- X-Tree Index Structure --- p.91 / Chapter 6.6.4 --- Compute GSOF and SOF --- p.95 / Chapter 6.6.5 --- Assign SO Values --- p.95 / Chapter 6.6.6 --- Multi-threads Programming --- p.96 / Chapter 6.7 --- Time Complexity --- p.97 / Chapter 6.8 --- Strength of SOF-Algorithm --- p.99 / Chapter 7 --- "Experiments on LOF' ，LOF"" and GridLOF" --- p.102 / Chapter 7.1 --- Datasets Used --- p.103 / Chapter 7.2 --- LOF' --- p.103 / Chapter 7.3 --- "LOF"" " --- p.109 / Chapter 7.4 --- GridLOF --- p.114 / Chapter 8 --- Empirical Results of SOF --- p.121 / Chapter 8.1 --- Synthetic Data Generation --- p.121 / Chapter 8.2 --- Experimental Setup --- p.124 / Chapter 8.3 --- Performance Measure --- p.124 / Chapter 8.3.1 --- Quality Measurement --- p.127 / Chapter 8.3.2 --- Scalability of SOF-Algorithm --- p.136 / Chapter 8.3.3 --- Effect of Parameters on SOF-Algorithm --- p.139 / Chapter 9 --- Conclusion --- p.140 / Bibliography --- p.142 / Publication --- p.149

Diss.-- Univ. of Innsbruck, 2008. / Includes bibliographical references and index.

The present investigation was a Monte Carlo experiment designed to evaluate the performance of several metrics in spotting correlational outliers. Specifically, the metrics that were compared were the Mahalanobis D², Bacon MLD, Carrig D, MCD, Robust PCLOW and Robust PCHIGH. This was the first comparative simulation study to include robust PCLOW and robust PCHIGH. The Mahalanobis D², MCD, Robust PCLOW and Robust PCHIGH were each applied using an approximate statistical criterion. The Carrig D and Bacon MLD were applied using a "natural drop" approach that separated scores on the metric into two groups: outlying and non-outlying. The "natural drop" utilizes a k-means algorithm from cluster analysis to separate the scores into the two groups. Both majority and contaminant observations were generated from multivariate normal distributions based on factor-analytic models. Experimental factors included majority versus contaminant communality level, majority-contaminant factor models scenario, number of variables, sample size and fraction of outliers. Results indicated that the "natural drop" method of application for the Carrig D and Bacon MLD leads to intolerably high false-alarm rates. Overall, PCLOW clearly outperformed PCHIGH. Suprisingly, PCLOW did not distinguish itself from MCD in terms of performance as expected in certain experimental conditions. The conditions in this study were limited. Future comparative studies of the metrics could include conditions of non-normality and hybrid types of outliers (i.e. outliers that are both mean shift and correlational). Despite its poor performance in this study, I theorize that robust PCHIGH could have an advantage over MCD in spotting certain kinds of mean-shift outliers. Also, research into the distributional properties of the Carrig D is warranted. / text

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