Local Distance Functions: A Taxonomy, New Algorithms, and an Evaluation

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 dimensionality reduction
and metric learning to ameliorate over-fitting. 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, which are then
interpolated during online classification. We also present a
comprehensive evaluation of all the algorithms on tasks in
face recognition, object recognition, and digit recognition.

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### Text Reference

Deva Ramanan and Simon Baker. Local distance functions: a taxonomy, new algorithms, and an evaluation. In*International Conference on Computer Vision (ICCV)*. 2009.

### BibTeX Reference

@inproceedings{RamananB_ICCV_2009,author = "Ramanan, Deva and Baker, Simon",

booktitle = "International Conference on Computer Vision (ICCV)",

title = "Local Distance Functions: A Taxonomy, New Algorithms, and an Evaluation",

year = "2009",

tag = "object_recognition"

}