A graph distance metric based on the maximal common subgraph
Pattern Recognition Letters
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Measuring Graph Similarity Using Spectral Geometry
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
On Euclidean Corrections for Non-Euclidean Dissimilarities
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Rectifying Non-Euclidean Similarity Data Using Ricci Flow Embedding
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
Non-Euclidean or non-metric measures can be informative
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Beyond Traditional Kernels: Classification in Two Dissimilarity-Based Representation Spaces
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Rectifying non-euclidean similarity data through tangent space reprojection
IbPRIA'11 Proceedings of the 5th Iberian conference on Pattern recognition and image analysis
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This paper concerns the analysis of patterns that are specified in terms of non-Euclidean dissimilarity or proximity rather than ordinal values. In prior work we have reported a means of correcting or rectifying the similarities so that the non-Euclidean artifacts are minimized. This is achieved by representing the data using a graph, and evolving the manifold embedding of the graph using Ricci flow. Although the method provides encouraging results, it can prove to be unstable. In this paper we explore how this problem can be overcome using a graph regularisation technique. Specifically, by regularising the curvature of the manifold on which the graph is embedded, then we can improve both the stability and performance of the method. We demonstrate the utility of our method on the standard "Chicken pieces" dataset and show that we can transform the non-Euclidean distances into Euclidean space.