Shared Gaussian Process Latent Variables Models - Oxford Brookes ...

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List of Figures 2.1 Volume ratio of hyper-cube and hyper-sphere . . . . . . . . . . . 16 2.2 Swissroll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3 Generative latent variable model . . . . . . . . . . . . . . . . . . 35 2.4 GTM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.5 Samples from GP Prior . . . . . . . . . . . . . . . . . . . . . . . 42 2.6 Samples from GP Posterior . . . . . . . . . . . . . . . . . . . . . 43 2.7 Probibalistic CCA . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.1 <strong>Shared</strong> back-constrained GP-LVM . . . . . . . . . . . . . . . . . 61 3.2 Toy data: generating signals . . . . . . . . . . . . . . . . . . . . 65 3.3 Toy data: observed data . . . . . . . . . . . . . . . . . . . . . . . 66 3.4 Toy data: latent embeddings . . . . . . . . . . . . . . . . . . . . 67 3.5 Toy data2: generating signals . . . . . . . . . . . . . . . . . . . . 68 3.6 Toy data2: observed data . . . . . . . . . . . . . . . . . . . . . . 68 3.7 Toy data2: latent embeddings . . . . . . . . . . . . . . . . . . . . 69 3.8 Toy data3: generating signals . . . . . . . . . . . . . . . . . . . . 70 3.9 Toy data3: observed data . . . . . . . . . . . . . . . . . . . . . . 71 3.10 Toy data3: latent embeddings . . . . . . . . . . . . . . . . . . . . 72 7
8 LIST OF FIGURES 3.11 Toy data3: latent embeddings . . . . . . . . . . . . . . . . . . . . 72 3.12 Subspace GP-LVM model . . . . . . . . . . . . . . . . . . . . . 74 4.1 NCCA model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.2 Toy data3: NCCA embedding . . . . . . . . . . . . . . . . . . . 88 4.3 Toy data3: observed data . . . . . . . . . . . . . . . . . . . . . . 88 4.4 Toy data3: Subspace GP-LVM embedding . . . . . . . . . . . . . 89 5.1 Kernel response matrix Poser pose data . . . . . . . . . . . . . . 102 5.2 Misinterpretation of angle error . . . . . . . . . . . . . . . . . . . 109 5.3 Poser single image results back-constrained GP-LVM . . . . . . . 110 5.4 Poser sequence image results back-constrained GP-LVM . . . . . 111 5.5 Kernel matrix back-constrained and subspace GP-LVM . . . . . . 114 5.6 Subspace GP-LVM pose inference . . . . . . . . . . . . . . . . . 115 5.7 Subspace GP-LVM ambiguity modeling . . . . . . . . . . . . . . 117
Page 1 and 2: Shared Gaussian Process Latent Vari
Page 3 and 4: Acknowledgements 2
Page 5 and 6: 4 CONTENTS 2.7.2 Training . . . . .
Page 7: 6 CONTENTS 5.10 Summary . . . . . .
Page 11 and 12: Chapter 1 Introduction Information
Page 13 and 14: 12 CHAPTER 1. INTRODUCTION current
Page 15 and 16: Chapter 2 Background 2.1 Introducti
Page 17 and 18: 16 CHAPTER 2. BACKGROUND 1 0.9 0.8
Page 19 and 20: 18 CHAPTER 2. BACKGROUND X to its o
Page 21 and 22: 20 CHAPTER 2. BACKGROUND dimensions
Page 23 and 24: 22 CHAPTER 2. BACKGROUND approximat
Page 25 and 26: 24 CHAPTER 2. BACKGROUND diagonal c
Page 27 and 28: 26 CHAPTER 2. BACKGROUND unraveled.
Page 29 and 30: 28 CHAPTER 2. BACKGROUND apply an a
Page 31 and 32: 30 CHAPTER 2. BACKGROUND be connect
Page 33 and 34: 32 CHAPTER 2. BACKGROUND Local Line
Page 35 and 36: 34 CHAPTER 2. BACKGROUND 15 10 5 0
Page 37 and 38: 36 CHAPTER 2. BACKGROUND by W, Figu
Page 39 and 40: 38 CHAPTER 2. BACKGROUND Figure 2.4
Page 41 and 42: 40 CHAPTER 2. BACKGROUND X ∈ ℜ
Page 43 and 44: 42 CHAPTER 2. BACKGROUND 2.5 2 1.5
Page 45 and 46: 44 CHAPTER 2. BACKGROUND rupted by
Page 47 and 48: 46 CHAPTER 2. BACKGROUND where ˜ C
Page 49 and 50: 48 CHAPTER 2. BACKGROUND prior over
Page 51 and 52: 50 CHAPTER 2. BACKGROUND generative
Page 53 and 54: 52 CHAPTER 2. BACKGROUND the latent
Page 55 and 56: 54 CHAPTER 2. BACKGROUND 2.9 Shared
Page 57 and 58: 56 CHAPTER 2. BACKGROUND Y X Figure
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58 CHAPTER 2. BACKGROUND Gaussian p
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60 CHAPTER 3. SHARED GP-LVM sponden
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62 CHAPTER 3. SHARED GP-LVM makes m
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64 CHAPTER 3. SHARED GP-LVM where t
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66 CHAPTER 3. SHARED GP-LVM 4 3 2 1
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68 CHAPTER 3. SHARED GP-LVM 1 0.8 0
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70 CHAPTER 3. SHARED GP-LVM Example
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72 CHAPTER 3. SHARED GP-LVM 0.3 0.2
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74 CHAPTER 3. SHARED GP-LVM φ Y X
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76 CHAPTER 3. SHARED GP-LVM leading
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78 CHAPTER 3. SHARED GP-LVM servati
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Chapter 4 NCCA 4.1 Introduction In
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82 CHAPTER 4. NCCA as u Y i = x S
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84 CHAPTER 4. NCCA X Y Z X X S Y Z
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86 CHAPTER 4. NCCA By pre-multiplyi
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88 CHAPTER 4. NCCA 1 0.8 0.6 0.4 0.
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90 CHAPTER 4. NCCA 4.5 Extensions W
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Chapter 5 Applications 5.1 Introduc
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94 CHAPTER 5. APPLICATIONS as optic
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96 CHAPTER 5. APPLICATIONS of an im
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98 CHAPTER 5. APPLICATIONS histogra
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100 CHAPTER 5. APPLICATIONS the dat
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102 CHAPTER 5. APPLICATIONS Figure
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104 CHAPTER 5. APPLICATIONS the GP
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106 CHAPTER 5. APPLICATIONS varianc
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108 CHAPTER 5. APPLICATIONS locatio
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112 CHAPTER 5. APPLICATIONS Error (
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116 CHAPTER 5. APPLICATIONS over th
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118 CHAPTER 5. APPLICATIONS age rep
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120 CHAPTER 6. CONCLUSIONS vated an
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122 CHAPTER 6. CONCLUSIONS a shared
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124 BIBLIOGRAPHY [7] S. Belongie, J
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126 BIBLIOGRAPHY [24] K. Grochow, S
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128 BIBLIOGRAPHY [39] D. MacKay. Ba
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130 BIBLIOGRAPHY [56] H. A. Simon.
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132 BIBLIOGRAPHY [74] S. Wachter an
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