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Content Provider | IEEE Xplore Digital Library |
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Author | Weiping Xu Hancock, E.R. Wilson, R.C. |
Copyright Year | 2010 |
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. |
Starting Page | 3324 |
Ending Page | 3327 |
File Size | 503067 |
Page Count | 4 |
File Format | |
ISBN | 9781424475421 |
ISSN | 10514651 |
e-ISBN | 9781424475414 |
DOI | 10.1109/ICPR.2010.812 |
Language | English |
Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Publisher Date | 2010-08-23 |
Publisher Place | Turkey |
Access Restriction | Subscribed |
Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subject Keyword | Manifolds Kernel Symmetric matrices Equations Euclidean distance Eigenvalues and eigenfunctions Computer science Ricci flow similarity embedding |
Content Type | Text |
Resource Type | Article |
Subject | Computer Vision and Pattern Recognition |
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