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Figure A.2: Truncated boundary of positive semidefinite cone in S 2 plotted in R 3 as (a, b, c). The boundary of S 2 + is the set of parameters (a, b, c) that satisfy a ≥ 0, c ≥ 0, ac = b 2 , it represents the set of symmetric PSD matrices that are not full rank. The interior of the cone is the set of positive definites matrices (S 2 ++ ).

Figure A.2: Truncated boundary of positive semidefinite cone in S 2 plotted in R 3 as (a, b, c). The boundary of S 2 + is the set of parameters (a, b, c) that satisfy a ≥ 0, c ≥ 0, ac = b 2 , it represents the set of symmetric PSD matrices that are not full rank. The interior of the cone is the set of positive definites matrices (S 2 ++ ).

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This thesis focuses on distance metric learning for image and webpage comparison. Distance metrics are used in many machine learning and computer vision contexts such as k-nearest neighbors classification, clustering, support vector machine, information/image retrieval, visualization etc. In this thesis, we focus on Mahalanobis-like distance metric...