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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326011 |
| Date | January 2007 |
| Contributors | Wang, Huan., Chinese University of Hong Kong Graduate School. Division of Information Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xiii, 119 leaves : ill. ; 30 cm. |
| Rights | Use 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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