DocumentCode :
2502224
Title :
Rectifying Non-Euclidean Similarity Data Using Ricci Flow Embedding
Author :
Xu, Weiping ; Hancock, Edwin R. ; Wilson, Richard C.
Author_Institution :
Dept. of Comput. Sci., Univ. of York, York, UK
fYear :
2010
fDate :
23-26 Aug. 2010
Firstpage :
3324
Lastpage :
3327
Abstract :
Similarity based pattern recognition is concerned with the analysis of patterns that are specified in terms of object dissimilarity or proximity rather than ordinal values. For many types of data and measures, these dissimilarities are not Euclidean. This hinders the use of many machine-learning techniques. In this paper, we provide a means of correcting or rectifying the similarities so that the non-Euclidean artifacts are minimized. We consider the data to be embedded as points on a curved manifold and then evolve the manifold so as to increase its flatness. Our work uses the idea of Ricci flow on the constant curvature Riemannian manifold to modify the Gaussian curvatures on the edges of a graph representing the non-Euclidean data. 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.
Keywords :
Gaussian processes; graph theory; image recognition; learning (artificial intelligence); Gaussian curvatures; Ricci flow embedding; chicken pieces dataset; constant curvature Riemannian manifold; graph; machine-learning techniques; nonEuclidean similarity data rectification; similarity based pattern recognition; Computer science; Eigenvalues and eigenfunctions; Equations; Euclidean distance; Kernel; Manifolds; Symmetric matrices; Ricci flow; embedding; similarity;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Pattern Recognition (ICPR), 2010 20th International Conference on
Conference_Location :
Istanbul
ISSN :
1051-4651
Print_ISBN :
978-1-4244-7542-1
Type :
conf
DOI :
10.1109/ICPR.2010.812
Filename :
5597159
Link To Document :
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