In many text mining applications involving high-dimensional feature space, it is difficult to collect sufficient training data for different domains. One strategy to tackle this problem is to intelligently adapt the trained model from one domain with labeled data to another domain with only unlabeled data. This strategy is known as domain adaptation. However, there are two major limitations of the existing domain adaptation approaches. The first limitation is that they all separate the domain adaptation framework into two separate steps. The first step attempts to minimize the domain gap, and then the second step is to train the predictive model based. on the reweighted instances or transformed feature representation. However, such a transformed representation may encode less information affecting the predictive performance. The second limitation is that they are restricted to using the first-order statistics in a Reproducing Kernel Hilbert Space (RKHS) to measure the distribution difference between the source domain and the target domain. In this thesis, we focus on developing solutions for those two limitations hindering the progress of domain adaptation techniques. / Then we propose an improved symmetric Stein's loss (SSL) function which combines the mean and covariance discrepancy into a unified Bregman matrix divergence of which Jensen-Shannon divergence between normal distributions is a particular case. Based on our proposed distribution gap measure based on second-order statistics, we present another new domain adaptation method called Location and Scatter Matching. The target is to find a good feature representation which can reduce the embedded distribution gap measured by SSL between the source domain and the target domain, at the same time, ensure the new derived representation can encode sufficient discriminants with respect to the label information. Then a standard machine learning algorithm, such as Support Vector Machine (SYM), can be adapted to train classifiers in the new feature subspace across domains. / We conduct a series of experiments on real-world datasets to demonstrate the performance of our proposed approaches comparing with other competitive methods. The results show significant improvement over existing domain adaptation approaches. / We develop a novel model to learn a low-rank shared concept space with respect to two criteria simultaneously: the empirical loss in the source domain, and the embedded distribution gap between the source domain and the target domain. Besides, we can transfer the predictive power from the extracted common features to the characteristic features in the target domain by the feature graph Laplacian. Moreover, we can kernelize our proposed method in the Reproducing Kernel Hilbert Space (RKHS) so as to generalize our model by making use of the powerful kernel functions. We theoretically analyze the expected error evaluated by common convex loss functions in the target domain under the empirical risk minimization framework, showing that the error bound can be controlled by the expected loss in the source domain, and the embedded distribution gap. / Chen, Bo. / Adviser: Wai Lam. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 87-95). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Lastly, in the context of motion deblurring, we discuss a few new motion deblurring problems that are significant to blur kernel estimation and nonblind deconvolution. We found that strong edges do not always profit kernel estimation, but instead under certain circumstance degrade it. This finding leads to a new metric to measure the usefulness of image edges in motion deblurring and a gradient selection process to mitigate their possible adverse effect. It makes possible to solve for very large blur PSFs which easily fail existing blind deblurring methods. We also propose an efficient and high-quality kernel estimation method based on the spatial prior and the iterative support detection (ISD) kernel refinement, which avoids hard threshold of the kernel elements to enforce sparsity. We employ the TV-ℓ1 deconvolution model, solved with a new variable substitution scheme to robustly suppress noise. / This thesis covers complete discussion of motion estimation and deblurring and presents new methods to tackle them. In the context of motion estimation, we study the problem of estimating 2D apparent motion from two or more input images, referred to as optical flow estimation. We discuss several specific fundamental problems in existing optical flow estimation frameworks, including 1) estimating flow vectors for textureless and occluded regions, which was regarded as infeasible and with large ambiguities, and 2) the incapability of the commonly employed coarse-to-fine multi-scale scheme to preserve motion structures in several challenging circumstances. / To address the problem of multi-scale estimation, we extend the coarse-to-fine scheme by complementing the initialization at each scale with sparse feature matching, based on the observation that fine motion structures, especially those with significant and abrupt displacement transition, cannot always be correctly reconstructed owing to an incorrect initialization. We also introduce the adaption of the objective function and development of a new optimization procedure, which constitute a unified system for both large- and small-displacement optical flow estimation. The effectiveness of our method is borne out by extensive experiments on small-displacement benchmark dataset as well as the challenging large-displacement optical flow data. / To further increase the sub-pixel accuracy, we study how resolution changes affect the flow estimates. We show that by simple upsampling, we can effectively reduce errors for sub-pixel correspondence. In addition, we identify the regularization bias problem and explore its relationship to the image resolution. We propose a general fine-to-coarse framework to compute sub-pixel color matching for different computer vision problems. Various experiments were performed on motion estimation and stereo matching data. We are able to reduce errors by up to 30%, which would otherwise be very difficult to achieve through other conventional optimization methods. / We propose novel methods to solve these problems. Firstly, we introduce a segmentation based variational model to regularize flow estimates for textureless and occluded regions. Parametric and Non-parametric optical flow models are combined, using a confidence map to measure the rigidity of the moving regions. The resulted flow field is with high quality even at motion discontinuity and textureless regions and is very useful for applications such as video editing. / Xu, Li. / Adviser: Jiaya Jia. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 126-137). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Finally, we study a multi-period, risk-averse inventory model. The objective is to maximize the expected pay-offs. The risk-averse behavior is modeled as to penalize the decision maker if a target-profit level is not satisfied for each financial reporting cycle. We recognize that the operational period is usually faster than the financial reporting cycle. Therefore, the financial reporting cycle can be considered as an integer times of the operational periods. We study this model under both accrual-basis accounting principle and cash-basis accounting principle. We prove that the optimal inventory policy is a state-dependent base-stock policy under the accrual-basis accounting method. We then show that the structure of an optimal policy is a complicated one for the cash-basis accounting method. / In this thesis we study three supply chain models which address downside risk from a different angle. We start with a commitment-option supply contract in a Conditional Value-at-Risk (CVaR) framework. We show that a CVaR trade-off analysis with advanced reservation can be carried out efficiently. Moreover, our study indicates how the corresponding contract decisions differ from decisions for optimizing an expected value. / Key words. Downside Risk Measure; CVaR; Risk; Loss-Averse; Dynamic Programming. / Owing to the growing globalization in economy and the advances in commerce, research in supply chain management has attracted large number of researchers in the last two decades. Yet standard treatments of supply chain models are mainly confined for the optimization of expected values with little reflection on risk considerations. Even for those that consider a risk measure in the objective function, there are quite few literatures employing downside risk measure. The downside risk measure takes into account only the part of the distribution that is below a critical value. Thus it indicates a safety-first strategy for decision maker. / The thesis is organized in five chapters. In Chapter 1, we provide the background and research motivation for considering downside risk measures in supply chain models. In Chapter 2, we study the pay-to-delay supply contracts with a Conditional Value-at-Risk (CVaR) framework. In Chapter 3, we study the loss-averse newsvendor problem. In Chapter 4, we extend the loss-averse model to a multi-period setting. We conclude the thesis in Chapter 5 with discussions for future research. / Then, we employ a loss-aversion utility function to characterize newsvendor's decision-making behavior. We find that when there is no shortage cost, the loss-averse newsvendor consistently orders less than a risk-neutral newsvendor. Further, we discover that the loss-averse newsvendor orders a constant quantity when the reference target is sufficiently large. We discuss the importance of initial inventory to achieve the target profit level. When the target is a decision variable, the newsvendor always sets the target no higher or no lower. / Ma, Lijun. / "October 2007." / Adviser: Houmin Yan. / Source: Dissertation Abstracts International, Volume: 69-08, Section: B, page: 5003. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 140-154). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Globalization of business results in significant changes and severe competition. These macro forces lead to international integration and improved performance standards. Products with contracting life cycles demand the whole supply chain to react effectively with flexibility. Together with the rapid development of information technology and recent moves in e-business, all these macro factors have forced business enterprises to restructure their supply chains. An important dimension of supply chain restructuring is to improve coordination amongst supply chain members to optimize overall performance. In many industries, we observe increasing activities in supply chain coordination through new coordination mechanisms and/or information sharing. At the same time, because incentives are not aligned, we also observe reluctance to adopt these new initiatives. / The main analytical results of this thesis are: (1) These new coordination mechanisms affect each supply chain member's payoff. However, as long as the stock level that upstream desires is higher than the one downstream desires, we find that upstream and downstream can always find a risk-sharing rule such that adoption of these new coordination mechanisms, along with the risk-sharing rule, will always lead to higher expected payoffs for both of the supply chain members. (2) Under those new coordination mechanisms, we find that, in general, if downstream receives a market demand signal that is greater than a cut off value, he will reveal it to upstream voluntarily; otherwise, he will not reveal. The cut off value is a function of downstream's information revealing cost, upstream's critical fractile and its prior belief of the demand signal. (3) We get similar results for the problem of capacity choice under traditional supply chain. But in this problem, whether or not downstream will share demand information to the upstream voluntarily is also dependent on downstream's critical fractile. / The main objective of this thesis is to model problems in supply chain regarding some new coordination mechanisms and information sharing to better understand the related incentive issues. We hope to identify some managerial insights to enhance better coordination within a supply chain. The main issues being addressed in this thesis are the followings: (1) There are new coordination mechanisms transferring the right to make stock level decision and the responsibility to keep stock to upstream. How will these changes influence incentives in the supply chain? Are there any arrangements such that all parties in a supply chain will be better off by adopting these new coordination mechanisms? (2) Transferring the responsibility to carry inventory from downstream to upstream often also requires information sharing but such information sharing may not be enforced by contract. In that case; will the downstream be willing to share information with the upstream voluntarily? (3) Demand information asymmetry also exists in traditional supply chain and upstream's capacity choice is heavily dependent on the demand information it obtained from downstream. What are the conditions for the downstream to voluntarily reveal the private information about demand? Knowing the answers to these questions help us to better understand incentive issues to enhance better supply chain coordination. / Chu Wai-hung Julius. / "Jun 2002." / Source: Dissertation Abstracts International, Volume: 63-10, Section: A, page: 3630. / Supervisor: Ching Chyi Lee. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 119-123). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

本論文討論了幾個重要的用於網絡分析的圖結構以及相闋的算法設計問題，並著重討論了其中的組合結構及其在大規模網絡中之計算問題。根據這些結構在網絡所處之層次，我們將它們分成局部結構和全局結構來分別討論。 / 對於在大規模網絡中的緊密子圖探測問題和極大完全子圖枚舉問題，本論文提出了新概念和新算法。其一，對於一種名為k-truss的新型緊密子圖，提出了更快的內存算法和適用於在大規模網絡中尋找此種子圖的方法。其二，針對於傳統完全子圖枚舉算法的輸出過大的問題，提出了用於緊湊表示圖中一切極大完全子圖的新方法。采用此種方法，我們能夠在保證重要信息得到保留的情況下，顯著地減小輸出的體積同時提高計算速度。 / This thesis discusses a number of important structures for network analysis and their algorithmic results. Special attentions are paid to combinatorial structures and related computation problems in large networks. According to the granularity of the concepts, we shall distinguish between local and global objects and present them separately. / New algorithms and concepts are proposed for interesting arising problems in cohesive subgraph detection and maximal clique enumeration (MCE). Specifically, algorithms for k-truss, a new type of cohesive subgraphs, are proposed including a fast in-memory algorithm and techniques that handle large disk-resident networks. Motivated by the sheer size of output by classic MCE algorithms, a novel notion for a low-redundancy representation of the set of all maximal cliques is proposed, which enables effective use of maximal cliques and a faster computation of the reduced output. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Jia. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 58-62). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.2 / Chapter 3 --- Global Structures --- p.3 / Chapter 3.1 --- Component Decomposition --- p.4 / Chapter 3.2 --- Structures with Hierarchy --- p.6 / Chapter 3.2.1 --- k-cores --- p.6 / Chapter 3.2.2 --- k-trusses --- p.8 / Chapter 3.3 --- Improved Truss Computation [45] --- p.10 / Chapter 3.3.1 --- Notations --- p.11 / Chapter 3.3.2 --- Faster In-Memory Algorithm --- p.11 / Chapter 3.3.3 --- Handling Massive Graphs --- p.16 / Chapter 3.3.4 --- Bottom-Up Approach --- p.17 / Chapter 3.3.5 --- Top-k Trusses --- p.23 / Chapter 3.3.6 --- Empirical Study --- p.28 / Chapter 3.4 --- Summary --- p.33 / Chapter 4 --- Local Structures --- p.33 / Chapter 4.1 --- Small Cycles and Clustering Coefficients --- p.33 / Chapter 4.2 --- Maximal Cliques --- p.36 / Chapter 4.3 --- Redundancy-Aware MCE [46] --- p.36 / Chapter 4.3.1 --- Motivations --- p.38 / Chapter 4.3.2 --- τ-visible MCE --- p.41 / Chapter 4.3.3 --- Applications --- p.50 / Chapter 4.3.4 --- Empirical Study --- p.52 / Chapter 4.4 --- Summary --- p.56 / Chapter 5 --- Structures in Mid-Zone --- p.56 / Chapter 5.1 --- Densest Subgraph --- p.56 / Chapter 5.2 --- Relaxed Cliques --- p.57 / Chapter 6 --- Concluding Remarks --- p.58

Huang Ming Xi = 三因結構模型之公司債劵定價及其應用 / 黃銘浠. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 99-102). / Text in English; abstracts in English and Chinese. / Huang Ming Xi = San yin jie gou mo xing zhi gong si zhai quan ding jia ji qi ying yong / Huang Mingxi. / Abstract --- p.i / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vii / List of Tables --- p.xiii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Structural Models of Credit Pricing --- p.3 / Chapter 2.1 --- Introduction --- p.3 / Chapter 2.2 --- Merton's Model (1974) --- p.4 / Chapter 2.2.1 --- The Framework of the Traditional Contingent Claims Analysis (CCA) --- p.5 / Chapter 2.2.2 --- The Valuation of Corporate Bonds with B-S Option Pric- ing Theory --- p.9 / Chapter 2.2.3 --- The Limitations of Traditional Contingent Claim Ap- proach --- p.12 / Chapter 2.3 --- "Shimko, Tejima and Deventer (1993)" --- p.15 / Chapter 2.3.1 --- The Merton's Model in a Stochastic Interest Rate Frame- work --- p.15 / Chapter 2.4 --- Longstaff and Schwartz (1995) --- p.17 / Chapter 2.4.1 --- A Structure Model of Early Default Mechanism and De- viations from APR --- p.17 / Chapter 2.5 --- Briys and de Varenne (1997) --- p.21 / Chapter 2.5.1 --- A Structure Model of Stochastic Default Barrier --- p.21 / Chapter 2.5.2 --- The Valuation of Risky Zero-Coupon Bonds --- p.22 / Chapter 2.6 --- Stationary-leverage-ratio Models --- p.25 / Chapter 2.6.1 --- Tauren (1999) --- p.25 / Chapter 2.6.2 --- Collin-Dufresne and Goldstein (2001) --- p.27 / Chapter 2.7 --- Summary --- p.29 / Chapter Chapter 3. --- The Valuation Framework of the Three-factor Model --- p.32 / Chapter 3.1 --- Introduction --- p.33 / Chapter 3.2 --- The Framework of the Three-factor Model --- p.35 / Chapter 3.3 --- The Valuation of Risky Bonds --- p.39 / Chapter 3.3.1 --- Imposing an Early Default Mechanism --- p.42 / Chapter 3.3.2 --- Application: The Valuation of Probability of Default --- p.45 / Chapter Chapter 4. --- The Pricing Methodology of the Three-factor Model --- p.46 / Chapter 4.1 --- Simplification of the Problem --- p.47 / Chapter 4.2 --- Methodology of Upper-lower Bound Scheme --- p.48 / Chapter 4.2.1 --- Single-stage Approximation --- p.48 / Chapter 4.2.2 --- Illustrative Examples --- p.53 / Chapter 4.2.3 --- Multistage Approximation --- p.54 / Chapter 4.2.4 --- Summary --- p.58 / Chapter 4.2.5 --- Systematic Multistage Estimation of Bond Price --- p.61 / Chapter 4.3 --- Estimation of Default Probability --- p.63 / Chapter Chapter 5. --- Numerical Results and Discussion --- p.69 / Chapter 5.1 --- Initial Setting of Parameters --- p.69 / Chapter 5.2 --- Numerical Results and Discussion --- p.74 / Chapter Chapter 6. --- Conclusion --- p.89 / Appendix A. The Derivation of the Three-Factor Model --- p.91 / Bibliography --- p.99

Photocopy of typescript. / Digitized by Kansas Correctional Industries

Li, Xu. / Thesis submitted in: December 2008. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 41-43). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background Study --- p.6 / Chapter 3 --- Model Formulation --- p.8 / Chapter 3.1 --- Trading Cost Function --- p.9 / Chapter 3.2 --- Notations and Optimality Equation --- p.11 / Chapter 4 --- Optimal Policy --- p.14 / Chapter 4.1 --- Preliminary Assumption and Results --- p.14 / Chapter 4.1.1 --- "Generalized (s, 5, H) Policy" --- p.14 / Chapter 4.1.2 --- Polya Distribution and Quasi-K-convex --- p.15 / Chapter 4.1.3 --- Assumptions --- p.20 / Chapter 4.2 --- Single Period Problem --- p.23 / Chapter 4.3 --- Finite-Period Problem --- p.30 / Chapter 4.4 --- The Algorithm --- p.36 / Chapter 5 --- Conclusion --- p.39 / Bibliography --- p.41

Hou, Wenting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 113-117). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Literature Review --- p.1 / Chapter 1.2 --- Problem Description --- p.8 / Chapter 1.3 --- The Main Contributions of This Thesis --- p.11 / Chapter 2 --- Model I --- p.13 / Chapter 2.1 --- Notation --- p.13 / Chapter 2.2 --- Model Formulation --- p.16 / Chapter 2.3 --- Analytical Solution --- p.19 / Chapter 3 --- Model II --- p.25 / Chapter 3.1 --- Model Formulation --- p.25 / Chapter 3.2 --- Analytical Solution --- p.30 / Chapter 3.3 --- How to Find y --- p.38 / Chapter 3.4 --- Numerical Example --- p.42 / Chapter 4 --- Model III --- p.47 / Chapter 4.1 --- Model Formulation --- p.48 / Chapter 4.2 --- Dynamic Programming --- p.50 / Chapter 4.2.1 --- DP I --- p.50 / Chapter 4.2.2 --- DP II --- p.53 / Chapter 4.3 --- Approximate Analytical Solution --- p.56 / Chapter 4.4 --- Computational Result Comparison --- p.65 / Chapter 5 --- Conclusions --- p.73 / Chapter A --- Source Data --- p.76 / Chapter A.l --- rti --- p.76 / Chapter A.2 --- qti --- p.79 / Chapter B --- Model II Numerical Example and Result --- p.82 / Chapter B. --- l Value of xti when A = 0.3 --- p.82 / Chapter B.2 --- Value of xti when A = 0.6 --- p.84 / Chapter B.3 --- Value of xti when A = 0.9 --- p.88 / Chapter B.4 --- True Value of xti --- p.91 / Chapter C --- Model III Numerical Example and Result --- p.98 / Chapter C.l --- The Value of Mt of DP II --- p.98 / Chapter C.2 --- Track of Optimal Value of DP II --- p.101 / Chapter C.3 --- The Optimal Total Wealth of DP II --- p.105 / Chapter C.4 --- The Optimal Asset Allocation of P4 --- p.109 / Bibliography --- p.113

Wang, Huan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 113-119). / Abstracts in English and Chinese. / Contents / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Learning Frameworks --- p.1 / Chapter 1.2 --- Sample Representation --- p.3 / Chapter 2 --- Background Study --- p.5 / Chapter 2.1 --- Tensor Algebra --- p.5 / Chapter 2.1.1 --- Tensor Unfolding (Flattening) --- p.6 / Chapter 2.1.2 --- Tensor Product --- p.6 / Chapter 2.2 --- Manifold Embedding and Dimensionality Reduction --- p.8 / Chapter 2.2.1 --- Principal Component Analysis (PCA) --- p.9 / Chapter 2.2.2 --- Metric Multidimensional Scaling (MDS) --- p.10 / Chapter 2.2.3 --- Isomap --- p.10 / Chapter 2.2.4 --- Locally Linear Embedding (LLE) --- p.11 / Chapter 2.2.5 --- Discriminant Analysis --- p.11 / Chapter 2.2.6 --- Laplacian Eigenmap --- p.14 / Chapter 2.2.7 --- Graph Embedding: A General Framework --- p.15 / Chapter 2.2.8 --- Maximum Variance Unfolding --- p.16 / Chapter 3 --- The Trace Ratio Optimization --- p.17 / Chapter 3.1 --- Introduction --- p.17 / Chapter 3.2 --- Dimensionality Reduction Formulations: Trace Ratio vs. Ratio Trace --- p.19 / Chapter 3.3 --- Efficient Solution of Trace Ratio Problem --- p.22 / Chapter 3.4 --- Proof of Convergency to Global Optimum --- p.23 / Chapter 3.4.1 --- Proof of the monotonic increase of λn --- p.23 / Chapter 3.4.2 --- Proof of Vn convergence and global optimum for λ --- p.24 / Chapter 3.5 --- Extension and Discussion --- p.27 / Chapter 3.5.1 --- Extension to General Constraints --- p.27 / Chapter 3.5.2 --- Discussion --- p.28 / Chapter 3.6 --- Experiments --- p.29 / Chapter 3.6.1 --- Dataset Preparation --- p.30 / Chapter 3.6.2 --- Convergence Speed --- p.31 / Chapter 3.6.3 --- Visualization of Projection Matrix --- p.31 / Chapter 3.6.4 --- Classification by Linear Trace Ratio Algorithms with Orthogonal Constraints --- p.33 / Chapter 3.6.5 --- Classification by Kernel Trace Ratio algorithms with General Constraints --- p.36 / Chapter 3.7 --- Conclusion --- p.36 / Chapter 4 --- A Convergent Solution to Tensor Subspace Learning --- p.40 / Chapter 4.1 --- Introduction --- p.40 / Chapter 4.2 --- Subspace Learning with Tensor Data --- p.43 / Chapter 4.2.1 --- Graph Embedding with Tensor Representation --- p.43 / Chapter 4.2.2 --- Computational Issues --- p.46 / Chapter 4.3 --- Solution Procedure and Convergency Proof --- p.46 / Chapter 4.3.1 --- Analysis of Monotonous Increase Property --- p.47 / Chapter 4.3.2 --- Proof of Convergency --- p.48 / Chapter 4.4 --- Experiments --- p.50 / Chapter 4.4.1 --- Data Sets --- p.50 / Chapter 4.4.2 --- Monotonicity of Objective Function Value --- p.51 / Chapter 4.4.3 --- Convergency of the Projection Matrices . . --- p.52 / Chapter 4.4.4 --- Face Recognition --- p.52 / Chapter 4.5 --- Conclusions --- p.54 / Chapter 5 --- Maximum Unfolded Embedding --- p.57 / Chapter 5.1 --- Introduction --- p.57 / Chapter 5.2 --- Maximum Unfolded Embedding --- p.59 / Chapter 5.3 --- Optimize Trace Ratio --- p.60 / Chapter 5.4 --- Another Justification: Maximum Variance Em- bedding --- p.60 / Chapter 5.5 --- Linear Extension: Maximum Unfolded Projection --- p.61 / Chapter 5.6 --- Experiments --- p.62 / Chapter 5.6.1 --- Data set --- p.62 / Chapter 5.6.2 --- Evaluation Metric --- p.63 / Chapter 5.6.3 --- Performance Comparison --- p.64 / Chapter 5.6.4 --- Generalization Capability --- p.65 / Chapter 5.7 --- Conclusion --- p.67 / Chapter 6 --- Regression on MultiClass Data --- p.68 / Chapter 6.1 --- Introduction --- p.68 / Chapter 6.2 --- Background --- p.70 / Chapter 6.2.1 --- Intuitive Motivations --- p.70 / Chapter 6.2.2 --- Related Work --- p.72 / Chapter 6.3 --- Problem Formulation --- p.73 / Chapter 6.3.1 --- Notations --- p.73 / Chapter 6.3.2 --- Regularization along Data Manifold --- p.74 / Chapter 6.3.3 --- Cross Manifold Label Propagation --- p.75 / Chapter 6.3.4 --- Inter-Manifold Regularization --- p.78 / Chapter 6.4 --- Regression on Reproducing Kernel Hilbert Space (RKHS) --- p.79 / Chapter 6.5 --- Experiments --- p.82 / Chapter 6.5.1 --- Synthetic Data: Nonlinear Two Moons . . --- p.82 / Chapter 6.5.2 --- Synthetic Data: Three-class Cyclones --- p.83 / Chapter 6.5.3 --- Human Age Estimation --- p.84 / Chapter 6.6 --- Conclusions --- p.86 / Chapter 7 --- Correspondence Propagation --- p.88 / Chapter 7.1 --- Introduction --- p.88 / Chapter 7.2 --- Problem Formulation and Solution --- p.92 / Chapter 7.2.1 --- Graph Construction --- p.92 / Chapter 7.2.2 --- Regularization on categorical Product Graph --- p.93 / Chapter 7.2.3 --- Consistency in Feature Domain and Soft Constraints --- p.96 / Chapter 7.2.4 --- Inhomogeneous Pair Labeling . --- p.97 / Chapter 7.2.5 --- Reliable Correspondence Propagation --- p.98 / Chapter 7.2.6 --- Rearrangement and Discretizing --- p.100 / Chapter 7.3 --- Algorithmic Analysis --- p.100 / Chapter 7.3.1 --- Selection of Reliable Correspondences . . . --- p.100 / Chapter 7.3.2 --- Computational Complexity --- p.102 / Chapter 7.4 --- Applications and Experiments --- p.102 / Chapter 7.4.1 --- Matching Demonstration on Object Recognition Databases --- p.103 / Chapter 7.4.2 --- Automatic Feature Matching on Oxford Image Transformation Database . --- p.104 / Chapter 7.4.3 --- Influence of Reliable Correspondence Number --- p.106 / Chapter 7.5 --- Conclusion and Future Works --- p.106 / Chapter 8 --- Conclusion and Future Work --- p.110 / Bibliography --- p.113