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

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1.3. NOTATIONS AND CONVENTIONS 13 3. C. H. Ek, P. Jaeckel, N. Campbell, N. Lawrence, and C. Melhuish. Shared Gaussian Process Latent Variable Models for Handling Ambiguous Facial Expressions. In AIP Conference Proceedings, volume 1107, page 147, 2009. 1.3 Notations and Conventions In the mathematical notation we use italics x to indicate scalars, bold lowercase x to indicate vectors, and bold uppercase X to indicate matrices. Vectors, unless stated otherwise, are column vectors. The transpose of a matrix is indicated by superscript X T . The identity matrix is represented by I. The vector ei represents the unit vector with all dimensions set to 0 except dimension i which is 1.
Chapter 2 Background 2.1 Introduction Modeling is the task of describing a system using a specific language. In this thesis the focus is on mathematical modeling which refers to the process of describing a system through the laws of mathematics. The building blocks of mathematical models are variables or parameter who by interaction through the law of mathematics aims to mimic the behavior of a system. There are many reasons why we are interested in creating accurate models of a specific system. A model allows us to analyze and and simulate the behavior of the system in a hypothetical scenario without having to jeopardize the actually system. A fundamental characteristic of a model are its degrees of freedom [22] which refers to the number of parameters or variables that are allowed to vary indepen- dently from each other. In many scenarios there is more than one way to describe a system, this can either be because different approximations or assumptions have been made or due to lack of knowledge of the system. For example, one set of 14
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 and 8: 6 CONTENTS 5.10 Summary . . . . . .
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64 CHAPTER 3. SHARED GP-LVM where t
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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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Chapter 5 Applications 5.1 Introduc
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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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