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Exploring intrinsic structures from samples: supervised, unsupervised, an semisupervised frameworks.

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

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326011
Date January 2007
ContributorsWang, Huan., Chinese University of Hong Kong Graduate School. Division of Information Engineering.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, xiii, 119 leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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