Hello everyone
Recently I mentioned metric learning as one of possible projects for this
years' GSoC, and would like to hear your comments.
Metric learning, as follows from the name, is about learning distance
functions. Usually the metric that is learned is a Mahalanobis metric, thus
the problem reduces to finding a PSD matrix A that minimizes some
functional.
Metric learning is usually done in a supervised way, that is, a user tells
which points should be closer and which should be more distant. It can be
expressed either in form of "similar" / "dissimilar", or "A is closer to B
than to C".
Since metric learning is (mostly) about a PSD matrix A, one can do Cholesky
decomposition on it to obtain a matrix G to transform the data. It could
lead to something like guided clustering, where we first transform the data
space according to our prior knowledge of similarity.
Metric learning seems to be quite an active field of research ([1
<http://www.icml2010.org/tutorials.html>], [2
<http://www.ariel.ac.il/sites/ofirpele/DFML_ECCV2010_tutorial/>], [3
<http://nips.cc/Conferences/2011/Program/event.php?ID=2543>]). There are 2
somewhat up-to date surveys: [1
<http://web.cse.ohio-state.edu/~kulis/pubs/ftml_metric_learning.pdf>] and [2
<http://arxiv.org/abs/1306.6709>].
Top 3 seemingly most cited methods (according to Google Scholar) are
- MMC by Xing et al.
<http://papers.nips.cc/paper/2164-distance-metric-learning-with-application-to-clustering-with-side-information.pdf>
This
is a pioneering work and, according to the survey #2
The algorithm used to solve (1) is a simple projected gradient approach
> requiring the full
>
> eigenvalue decomposition of
>
> M
>
> at each iteration. This is typically intractable for medium
>
> and high-dimensional problems
- Large Margin Nearest Neighbor by Weinberger et al
<http://papers.nips.cc/paper/2795-distance-metric-learning-for-large-margin-nearest-neighbor-classification.pdf>.
The survey 2 acknowledges this method as "one of the most widely-used
Mahalanobis distance learning methods"
LMNN generally performs very well in practice, although it is sometimes
> prone to overfitting due to the absence of regularization, especially in
> high dimension
- Information-theoretic metric learning by Davis et al.
<http://dl.acm.org/citation.cfm?id=1273523> This one features a special
kind of regularizer called logDet.
- There are many other methods. If you guys know that other methods
rock, let me know.
So the project I'm proposing is about implementing 2nd or 3rd (or both?)
algorithms along with a relevant transformer.
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