Support Vector Machines (MAHOUT) edited by David Houghton
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http://cwiki.apache.org/confluence/display/MAHOUT/Support+Vector+Machines
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http://cwiki.apache.org/confluence/pages/diffpagesbyversion.action?pageId=75683&originalVersion=2&revisedVersion=3
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h1. Support Vector Machines
As with Naive Bayes, Support Vector Machines (or SVMs in short) can be used to
solve the task of assigning objects to classes. However, the way this task is
solved is completely different to the setting in Naive Bayes.
Each object is considered to be a point in _n_ dimensional feature space, _n_
being the number of features used to describe the objects numerically. In
addition each object is assigned a binary label, let us assume the labels are
"positive" and "negative". During learning, the algorithm tries to find a
hyperplane in that space, that perfectly separates positive from negative
objects.
It is trivial to think of settings where this might very well be impossible. To
remedy this situation, objects can be assigned so called slack terms, that
punish mistakes made during learning appropriately. That way, the algorithm is
forced to find the hyperplane that causes the least number of mistakes.
Another way to overcome the problem of there being no linear hyperplane to
separate positive from negative objects is to simply project each feature
vector into an higher dimensional feature space and search for a linear
separating hyperplane in that new space. Usually the main problem with learning
in high dimensional feature spaces is the so called curse of dimensionality.
That is, there are fewer learning examples available than free parameters to
tune. In the case of SVMs this problem is less detrimental, as SVMs impose
additional structural constraints on their solutions. Each separating
hyperplane needs to have a maximal margin to all training examples. In
addition, that way, the solution may be based on the information encoded in
only very few examples.
h2. Strategy for parallelization
h2. Design of packages
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