A stochastic self-organizing map for proximity data
Neural Computation
How to make large self-organizing maps for nonvectorial data
Neural Networks - New developments in self-organizing maps
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
The Journal of Machine Learning Research
The Dissimilarity Representation for Pattern Recognition: Foundations And Applications (Machine Perception and Artificial Intelligence)
On the information and representation of non-Euclidean pairwise data
Pattern Recognition
Edit distance-based kernel functions for structural pattern classification
Pattern Recognition
Simpler core vector machines with enclosing balls
Proceedings of the 24th international conference on Machine learning
On sampling-based approximate spectral decomposition
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Similarity-based Classification: Concepts and Algorithms
The Journal of Machine Learning Research
Topographic mapping of large dissimilarity data sets
Neural Computation
Non-Euclidean dissimilarities: causes and informativeness
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Clustered Nyström method for large scale manifold learning and dimension reduction
IEEE Transactions on Neural Networks
Beyond Traditional Kernels: Classification in Two Dissimilarity-Based Representation Spaces
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
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Domain specific (dis-)similarity or proximity measures, employed e.g. in alignment algorithms in bio-informatics, are often used to compare complex data objects and to cover domain specific data properties. Lacking an underlying vector space, data are given as pairwise (dis-)similarities. The few available methods for such data do not scale well to very large data sets. Kernel methods easily deal with metric similarity matrices, also at large scale, but costly transformations are necessary starting with non-metric (dis-) similarities. We propose an integrative combination of Nyström approximation, potential double centering and eigenvalue correction to obtain valid kernel matrices at linear costs. Accordingly effective kernel approaches, become accessible for these data. Evaluation at several larger (dis-)similarity data sets shows that the proposed method achieves much better runtime performance than the standard strategy while keeping competitive model accuracy. Our main contribution is an efficient linear technique, to convert (potentially non-metric) large scale dissimilarity matrices into approximated positive semi-definite kernel matrices.