The algebraic eigenvalue problem
The algebraic eigenvalue problem
A Divide-and-Conquer Algorithm for the Symmetric TridiagonalEigenproblem
SIAM Journal on Matrix Analysis and Applications
The nature of statistical learning theory
The nature of statistical learning theory
Classification on pairwise proximity data
Proceedings of the 1998 conference on Advances in neural information processing systems II
The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Efficient Pattern Recognition Using a New Transformation Distance
Advances in Neural Information Processing Systems 5, [NIPS Conference]
A generalized kernel approach to dissimilarity-based classification
The Journal of Machine Learning Research
Optimal Cluster Preserving Embedding of Nonmetric Proximity Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Enhanced Perceptual Distance Functions and Indexing for Image Replica Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature Space Interpretation of SVMs with Indefinite Kernels
IEEE Transactions on Pattern Analysis and Machine Intelligence
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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Many emerging applications formulate non-metric proximity matrices (non-positive semidefinite), and hence cannot fit into the framework of kernel machines. A popular approach to this problem is to transform the spectrum of the similarity matrix so as to generate a positive semidefinite kernel matrix. In this paper, we explore four representative transformation methods: denoise, flip, diffusion, and shift. Theoretically, we discuss a generalization problem where the test data are not available during transformation, and thus propose an efficient algorithm to address the problem of updating the cross-similarity matrix between test and training data. Extensive experiments have been conducted to evaluate the performance of these methods on several real-world (dis)similarity matrices with semantic meanings.