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\title{Project Progress Summary}
\author{Matthew Gray}

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I'm going to be looking at the gesture classification problem.
\par

Looking at the data, it appears to be a good candidate for clustering,
as the classes are reasonably well seperated.  Further, I wanted to
try implementing an algorithm described in a paper I
read.\footnote{``Nonlinear Component Analysis as a Kernel Eigenvalue
Problem'', Bernhard Sch\"olkopf, Alexander Smola, Klaus-Robert
M\"uller, December 1996} The paper uses a kernel approach to create a large feature
space for principal component analysis, in a way similar to what is
used in nonlinear Support Vector Machines.  This algorithm is
implemented for the paper.  Also in the paper, it suggests this
approach might be successful with clustering algorithms as well.
\par
Essentially the ``trick'' involves reformulating clustering (initially
I will do non-linear k-means, and time permitting, nonlinear GMMs) in
terms of the dot product of observations transformed into a
high-dimensional feature space.  Normally using such a
high-dimensional feature space would be prohibitively expensive
computationally.  These dot products of features can be replaced with
a kernel function, greatly reducing the computational complexity.
\par
As a preliminary exercise, I implemented straightforward linear
k-means clustering as a guage of what kind of minimum performance
could be expected. With 40 means, and without composing the
observations into any sort of lag space, k-means gives 13\% error on
out-of-sample data, after assigning each cluster the class of its
dominant population from the training set.

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