by Wong, Wai-Chiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 89-94). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgments --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Document Clustering --- p.2 / Chapter 1.2 --- DC-tree --- p.4 / Chapter 1.3 --- Feature Extraction --- p.5 / Chapter 1.4 --- Outline of the Thesis --- p.5 / Chapter 2 --- Related Work --- p.8 / Chapter 2.1 --- Clustering Algorithms --- p.8 / Chapter 2.1.1 --- Partitional Clustering Algorithms --- p.8 / Chapter 2.1.2 --- Hierarchical Clustering Algorithms --- p.10 / Chapter 2.2 --- Document Classification by Examples --- p.11 / Chapter 2.2.1 --- k-NN algorithm - Expert Network (ExpNet) --- p.11 / Chapter 2.2.2 --- Learning Linear Text Classifier --- p.12 / Chapter 2.2.3 --- Generalized Instance Set (GIS) algorithm --- p.12 / Chapter 2.3 --- Document Clustering --- p.13 / Chapter 2.3.1 --- B+-tree-based Document Clustering --- p.13 / Chapter 2.3.2 --- Suffix Tree Clustering --- p.14 / Chapter 2.3.3 --- Association Rule Hypergraph Partitioning Algorithm --- p.15 / Chapter 2.3.4 --- Principal Component Divisive Partitioning --- p.17 / Chapter 2.4 --- Projections for Efficient Document Clustering --- p.18 / Chapter 3 --- Background --- p.21 / Chapter 3.1 --- Document Preprocessing --- p.21 / Chapter 3.1.1 --- Elimination of Stopwords --- p.22 / Chapter 3.1.2 --- Stemming Technique --- p.22 / Chapter 3.2 --- Problem Modeling --- p.23 / Chapter 3.2.1 --- Basic Concepts --- p.23 / Chapter 3.2.2 --- Vector Model --- p.24 / Chapter 3.3 --- Feature Selection Scheme --- p.25 / Chapter 3.4 --- Similarity Model --- p.27 / Chapter 3.5 --- Evaluation Techniques --- p.29 / Chapter 4 --- Feature Extraction and Weighting --- p.31 / Chapter 4.1 --- Statistical Analysis of the Words in the Web Domain --- p.31 / Chapter 4.2 --- Zipf's Law --- p.33 / Chapter 4.3 --- Traditional Methods --- p.36 / Chapter 4.4 --- The Proposed Method --- p.38 / Chapter 4.5 --- Experimental Results --- p.40 / Chapter 4.5.1 --- Synthetic Data Generation --- p.40 / Chapter 4.5.2 --- Real Data Source --- p.41 / Chapter 4.5.3 --- Coverage --- p.41 / Chapter 4.5.4 --- Clustering Quality --- p.43 / Chapter 4.5.5 --- Binary Weight vs Numerical Weight --- p.45 / Chapter 5 --- Web Document Clustering Using DC-tree --- p.48 / Chapter 5.1 --- Document Representation --- p.48 / Chapter 5.2 --- Document Cluster (DC) --- p.49 / Chapter 5.3 --- DC-tree --- p.52 / Chapter 5.3.1 --- Tree Definition --- p.52 / Chapter 5.3.2 --- Insertion --- p.54 / Chapter 5.3.3 --- Node Splitting --- p.55 / Chapter 5.3.4 --- Deletion and Node Merging --- p.56 / Chapter 5.4 --- The Overall Strategy --- p.57 / Chapter 5.4.1 --- Preprocessing --- p.57 / Chapter 5.4.2 --- Building DC-tree --- p.59 / Chapter 5.4.3 --- Identifying the Interesting Clusters --- p.60 / Chapter 5.5 --- Experimental Results --- p.61 / Chapter 5.5.1 --- Alternative Similarity Measurement : Synthetic Data --- p.61 / Chapter 5.5.2 --- DC-tree Characteristics : Synthetic Data --- p.63 / Chapter 5.5.3 --- Compare DC-tree and B+-tree: Synthetic Data --- p.64 / Chapter 5.5.4 --- Compare DC-tree and B+-tree: Real Data --- p.66 / Chapter 5.5.5 --- Varying the Number of Features : Synthetic Data --- p.67 / Chapter 5.5.6 --- Non-Correlated Topic Web Page Collection: Real Data --- p.69 / Chapter 5.5.7 --- Correlated Topic Web Page Collection: Real Data --- p.71 / Chapter 5.5.8 --- Incremental updates on Real Data Set --- p.72 / Chapter 5.5.9 --- Comparison with the other clustering algorithms --- p.73 / Chapter 6 --- Conclusion --- p.75 / Appendix --- p.77 / Chapter A --- Stopword List --- p.77 / Chapter B --- Porter's Stemming Algorithm --- p.81 / Chapter C --- Insertion Algorithm --- p.83 / Chapter D --- Node Splitting Algorithm --- p.85 / Chapter E --- Features Extracted in Experiment 4.53 --- p.87 / Bibliography --- p.88

Wong Yuen Kwan Virginia. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 85-86). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Deletion and Distance Measure --- p.6 / Chapter 2.1 --- Mahalanobis and Cook's Distances --- p.6 / Chapter 2.2 --- Defining New Measure Di --- p.8 / Chapter 2.3 --- Derivation of cov(s(i) ´ؤ s) --- p.10 / Chapter 3 --- Procedures for Detecting Influential Observations --- p.18 / Chapter 3.1 --- The One-Step Method --- p.18 / Chapter 3.1.1 --- The Method --- p.18 / Chapter 3.1.2 --- Design of Simulation Studies --- p.19 / Chapter 3.1.3 --- Results of Simulation Studies --- p.21 / Chapter 3.1.4 --- Higher Dimensional Cases --- p.24 / Chapter 3.2 --- The Forward Search Procedure --- p.24 / Chapter 3.2.1 --- Idea of the Forward Search Procedure --- p.25 / Chapter 3.2.2 --- The Algorithm --- p.26 / Chapter 4 --- Examples and Observations --- p.29 / Chapter 4.1 --- Example 1: Brain and Body Weight Data --- p.29 / Chapter 4.2 --- Example 2: Stack Loss Data --- p.34 / Chapter 4.3 --- Example 3: Percentage of Cloud Cover --- p.40 / Chapter 4.4 --- Example 4: Synthetic data of Hawkins et al.(1984) . --- p.46 / Chapter 4.5 --- Observations and Comparison --- p.52 / Chapter 5 --- Discussion and Conclusion --- p.54 / Tables --- p.56 / Figures --- p.77 / Bibliography --- p.85

by Kwan Yee Ting, Chris. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 44-48). / Abstract also in Chinese. / Acknowledgements --- p.i / Abstract --- p.ii / Table of Contents --- p.v / List of Figures --- p.ix / List of Tables --- p.x / Chapter Part 1. --- Introduction --- p.1 / Chapter 1.1 --- Identification of TCM --- p.1 / Chapter 1.2 --- Chemical Pattern Recognition --- p.2 / Chapter 1.3 --- Discriminant Analysis --- p.3 / Chapter 1.4 --- Epimedium --- p.5 / Chapter 1.5 --- High Performance Liquid Chromatography --- p.6 / Chapter 1.6 --- Objectives of this work --- p.8 / Chapter Part 2. --- Chemical Analysis --- p.9 / Chapter 2.1 --- Sources of Epimedium samples --- p.9 / Chapter 2.2 --- Extraction --- p.9 / Chapter 2.2.1 --- Sample Pre-treatment --- p.9 / Chapter 2.2.2 --- Extraction Procedure --- p.9 / Chapter 2.2.3 --- Extraction Recovery --- p.11 / Chapter 2.3 --- Instrumental Analysis --- p.11 / Chapter 2.3.1 --- Chromatographic Operating Conditions --- p.12 / Chapter 2.3.2 --- Preparation of Calibration Graph --- p.12 / Chapter 2.3.3 --- Sample injection --- p.13 / Chapter 2.4 --- Results and Discussion --- p.13 / Chapter 2.4.1 --- Linearity of the Calibration Graph --- p.13 / Chapter 2.4.2 --- Development of Analysis Procedure --- p.15 / Chapter 2.4.2.1 --- Sample Pre-treatment --- p.15 / Chapter 2.4.2.2 --- Extractant --- p.15 / Chapter 2.4.2.3 --- Purification of Extract --- p.15 / Chapter 2.4.2.4 --- Extraction Time --- p.17 / Chapter 2.4.2.5 --- Solvent Gradient --- p.18 / Chapter 2.4.2.6 --- Detection --- p.19 / Chapter 2.4.3 --- Quantitative Analysis --- p.19 / Chapter 2.4.3.1 --- Extraction Recovery --- p.19 / Chapter 2.4.3.2 --- Icariin Content --- p.20 / Chapter 2.5 --- Conclusions --- p.22 / Chapter Part 3. --- Chemical Pattern Recognition --- p.24 / Chapter 3.1 --- Materials and Methods --- p.24 / Chapter 3.1.1 --- Chromatographic Results --- p.24 / Chapter 3.1.2 --- Patterns of Epimedium Samples --- p.24 / Chapter 3.1.3 --- Computer Program --- p.25 / Chapter 3.1.4 --- Variable Extraction --- p.25 / Chapter 3.1.4.1 --- Variable Extraction Parameters --- p.25 / Chapter 3.1.4.2 --- Variable Extraction Methods --- p.26 / Chapter 3.1.4.3 --- Transformation of Variables --- p.27 / Chapter 3.1.5 --- Variable Selection --- p.27 / Chapter 3.1.6 --- Predictive Power of the Recognition Model --- p.28 / Chapter 3.2 --- Results --- p.28 / Chapter 3.2.1 --- Accuracy of the Recognition Models --- p.28 / Chapter 3.2.2 --- Classification Functions --- p.29 / Chapter 3.2.3 --- Casewise Results of Recognition Model IV --- p.31 / Chapter 3.2.4 --- Plotting of the Best Two Canonical Discriminant Functions --- p.33 / Chapter 3.3 --- Discussion --- p.33 / Chapter 3.3.1 --- Meaning of Extracted Variables --- p.33 / Chapter 3.3.2 --- Limitations of Variable Extraction Methods --- p.34 / Chapter 3.3.3 --- Importance of the Variable Extraction Methods --- p.34 / Chapter 3.3.4 --- "Reasons for the Poor Performance in Recognition Models I, II and III" --- p.35 / Chapter 3.3.5 --- Selected Variables in Model IV --- p.35 / Chapter 3.3.6 --- Misclassified Samples --- p.36 / Chapter 3.3.7 --- Quality Assessment --- p.38 / Chapter 3.3.8 --- Comparison with Another Chemical Pattern Recognition Method for the Identification of Epimedium --- p.39 / Chapter 3.3.9 --- Potential Usage of the Pattern Recognition Method --- p.42 / Chapter 3.3.10 --- Advantage of the Pattern Recognition Method --- p.42 / Chapter 3.3.11 --- Disadvantage of Discriminant Analysis --- p.42 / Chapter 3.4 --- Conclusions --- p.43 / References --- p.44 / Appendix I Epimedium Species in China --- p.49 / Appendix II --- p.50 / Chapter II.1 --- Chromatograms of Samples of Epimedium sagittatum --- p.50 / Chapter II.2 --- Chromatograms of Samples of Epimedium pubescens --- p.57 / Chapter II.3 --- Chromatograms of Samples of Epimedium koreanum --- p.61 / Chapter II.4 --- Chromatograms of Samples of Epimedium leptorrhizum --- p.67 / Chapter II.5 --- Chromatograms of Samples of Epimedium wnshanese --- p.69 / Chapter II.6 --- Chromatograms of Samples of Epimedium brevicornum --- p.72 / Appendix III Log-transformed Values of Variables --- p.75

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Digitized by Kansas Correctional Industries

Digitized by Kansas Correctional Industries

The overall theme of this thesis work concerns the problem of handling measurement error and sources of variation in functional data models. The first part introduces a wavelet-based sparse principal component analysis approach for characterizing the variability of multilevel functional data that are characterized by spatial heterogeneity and local features. The total covariance of the data can be decomposed into three hierarchical levels: between subjects, between sessions and measurement error. Sparse principal component analysis in the wavelet domain allows for reducing dimension and deriving main directions of random effects that may vary for each hierarchical level. The method is illustrated by application to data from a study of human vision. The second part considers the problem of scalar-on-function regression when the functional regressors are observed with measurement error. We develop a simulation-extrapolation method for scalar-on-function regression, which first estimates the error variance, establishes the relationship between a sequence of added error variance and the corresponding estimates of coefficient functions, and then extrapolates to the zero-error. We introduce three methods to extrapolate the sequence of estimated coefficient functions. In a simulation study, we compare the performance of the simulation-extrapolation method with two pre-smoothing methods based on smoothing splines and functional principal component analysis. The third part discusses several extensions of the simulation-extrapolation method developed in the second part. Some of the extensions are illustrated by application to diffusion tensor imaging data.

Inner hair cells (IHCs) are the actual sensory receptors in hearing. Immature IHCs generate spontaneous calcium-dependent action potentials. Changing the characteristic of the Ca2Å signals modulates the amplitude and duration of the action potentials in these cells. These spontaneous action potential firing patterns are thought to be important for the development of the auditory system. The aim of this thesis is to gain a deeper understanding of the electrical activity and calcium signalling during development of IHCs from a mathematical point of view. A numerical bifurcation analysis is performed to delineate the relative contributions of the model parameters to the asymptotic behaviour of the model. In particular, we investigate the pattern of periodic solutions including single (normal) spiking, pseudoplateau burstings and complex solutions using two-parameter sections of the parameter space. We also demonstrate that a simplified (three-dimensional) model can generate similar dynamics as the original (four-dimensional) IHC model. This reduced model could be characterised by two fast and one slow or one fast and two slow variables depending on the parameters’ choice. Hence, the mechanisms underlying the bursting dynamics and mixed mode oscillations in the model are studied applying 1-slow/2-fast and 2-slow/1-fast analysis, respectively.

In this thesis, I develop a valuation model to price convertible bonds with call provision. Convertible bonds are hybrid instruments that possess both equity and debt characteristics. The purpose of this study is to build a pricing model for convertible and callable bonds and to compare the mathematical results of the model with real world market performance. I construct a two-factor valuation model, in which both the interest rate and the stock price are stochastic. I derive the partial differential equation of two stochastic variables and state the final and boundary conditions of the convertible bond using the mean reversion model on interest rate. Because it is difficult to obtain a closed solution for the American convertible bond due to its structural complexity, I use the binomial tree model to value the convertible bond by constructing the interest rate tree and stock price tree. As a convertible bond is a hybrid security of debt and equity, I combine the interest rate tree and stock price tree into one single tree. Default risk is added to the valuation tree to represent the event of a default. The model is then tested and compared with the performance of the Canadian convertible bond market. Moreover, I study the duration, convexity and Greeks of convertible bonds. These are important risk metrics in the portfolio management of the convertible bond to measure risks linked to interest rate, equity, volatility and other market factors. I investigate the partial derivative of the value of the convertible bond with respect to various parameters, such as the interest rate, stock price, volatility of the interest rate, volatility of the stock price, mean reversion of the interest rate and dividend yield of the underlying stock. A convertible bond arbitrage portfolio is constructed to capture the abnormal returns from the Delta hedging strategy and I describe the risks associated with these returns. The portfolio is created by matching long positions in convertible bonds, with short positions in the underlying stock to create a Delta hedged convertible bond position, which captures income and volatility.

by Ka-Kit Tse. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references. / Acknowledgments --- p.i / List of tables --- p.v / Chapter Chapter 1: --- Overall Review --- p.1 / Chapter Chapter 2: --- Essay one - A Mathematical Programming Approach to Clusterwise Regression Model and its Extensions / Chapter 2.0. --- Abstract --- p.5 / Chapter 2.1. --- Introduction --- p.6 / Chapter 2.2. --- A Mathematical Programming Formulation of the Clusterwise Regression Model --- p.10 / Chapter 2.2.1. --- The Generalized Clusterwise Regression Model --- p.10 / Chapter 2.2.2. --- "Clusterwise Regression Model (Spath, 1979)" --- p.14 / Chapter 2.2.3. --- A Nonparametric Clusterwise Regression Model --- p.15 / Chapter 2.2.4. --- A Mixture Approach to Clusterwise Regression Model --- p.16 / Chapter 2.2.5. --- An Illustrative Application --- p.19 / Chapter 2.3. --- Mathematical Programming Formulation of the Clusterwise Discriminant Analysis --- p.21 / Chapter 2.4. --- Conclusion --- p.25 / Chapter 2.5. --- Appendix --- p.28 / Chapter 2.6. --- References --- p.32 / Chapter 2.7. --- Tables --- p.35 / Chapter Chapter 3: --- Essay two - A Mathematical Programming Approach to Clusterwise Rank Order Logit Model / Chapter 3.0. --- Abstract --- p.40 / Chapter 3.1. --- Introduction --- p.41 / Chapter 3.2. --- Clusterwise Rank Order Logit Model --- p.42 / Chapter 3.3. --- Numerical Illustration --- p.46 / Chapter 3.4. --- Conclustion --- p.48 / Chapter 3.5. --- References --- p.50 / Chapter 3.6. --- Tables --- p.52 / Chapter Chapter 4: --- Essay three - A Mathematical Programming Approach to Metric Unidimensional Scaling / Chapter 4.0. --- Abstract --- p.53 / Chapter 4.1. --- Introduction --- p.54 / Chapter 4.2. --- Nonlinear Programming Formulation --- p.56 / Chapter 4.3. --- Numerical Examples --- p.60 / Chapter 4.4. --- Possible Extensions --- p.61 / Chapter 4.5. --- Conclusion and Extensions --- p.63 / Chapter 4.6. --- References --- p.64 / Chapter 4.7. --- Tables --- p.66 / Chapter Chapter 5: --- Research Project in Progress / Chapter 5.1. --- Project 1 -- An Integrated Approach to Taste Test Experiment Within the Prospect Theory Framework --- p.68 / Chapter 5.1.1. --- Experiment Procedure --- p.68 / Chapter 5.1.2. --- Experimental Result --- p.72 / Chapter 5.2. --- Project 2 -- An Integrated Approach to Multi- Dimensional Scaling Problem --- p.75 / Chapter 5.2.1. --- Introduction --- p.75 / Chapter 5.2.2. --- Experiment Procedure --- p.76 / Chapter 5.2.3. --- Questionnaire --- p.78 / Chapter 5.2.4. --- Experimental Result --- p.78