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Issue No. 04 - April (2011 vol. 33)
ISSN: 0162-8828
pp: 794-806
Deva Ramanan , University of California Irvine, Irvine
Simon Baker , Microsoft Research, Redmond
ABSTRACT
We present a taxonomy for local distance functions where most existing algorithms can be regarded as approximations of the geodesic distance defined by a metric tensor. We categorize existing algorithms by how, where, and when they estimate the metric tensor. We also extend the taxonomy along each axis. How: We introduce hybrid algorithms that use a combination of techniques to ameliorate overfitting. Where: We present an exact polynomial-time algorithm to integrate the metric tensor along the lines between the test and training points under the assumption that the metric tensor is piecewise constant. When: We propose an interpolation algorithm where the metric tensor is sampled at a number of references points during the offline phase. The reference points are then interpolated during the online classification phase. We also present a comprehensive evaluation on tasks in face recognition, object recognition, and digit recognition.
INDEX TERMS
Nearest neighbor classification, metric learning, metric tensor, local distance functions, taxonomy, database, evaluation.
CITATION
Deva Ramanan, Simon Baker, "Local Distance Functions: A Taxonomy, New Algorithms, and an Evaluation", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 33, no. , pp. 794-806, April 2011, doi:10.1109/TPAMI.2010.127
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