Hey.
I am not very familiar with the literature on metric learning, but I
think one thing that we need to think about before
is what the interface would be.
We really want something that works in a .fit().predict() or
.fit().transform() way.
I guess you could do "transform" to get the distances to the training
data (is that what one would want?)
But how would the labels for the "fit" look like?
Cheers,
Andy
On 03/18/2015 08:39 AM, Artem wrote:
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/%7Ekulis/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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