Commit 71c2b029 authored by Davis King's avatar Davis King

Clarified docs.

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parent a033cd99
......@@ -556,39 +556,40 @@ Davis E. King. <a href="http://www.jmlr.org/papers/volume10/king09a/king09a.pdf"
usually called regularization.
</p>
<p>
In the above setting all the training data consists of labeled samples.
However, it would be nice to be able to benefit from unlabeled data
(see the <a href="linear_manifold_regularizer_ex.cpp.html">example program</a>
for this object for an example where unlabeled
data is useful). The idea of manifold regularization is to extract useful
information from unlabeled data by defining which data samples are "close"
to each other (perhaps by using their 3 <a href="#find_k_nearest_neighbors">nearest neighbors</a>)
and then adding a term to the loss function that penalizes any decision rule which produces
different output on data samples that we have designated as being close.
<p>
In the above setting, all the training data consists of labeled samples.
However, it would be nice to be able to benefit from unlabeled data.
The idea of manifold regularization is to extract useful information from
unlabeled data by defining which data samples are "close" to each other
(perhaps by using their 3 <a href="#find_k_nearest_neighbors">nearest neighbors</a>)
and then adding a term to
the loss function that penalizes any decision rule which produces
different outputs on data samples which we have designated as being close.
</p>
<p>
It turns out that it is possible to turn these manifold regularized loss
functions into the normal form shown above by applying a certain kind
of processing to all of our data samples. Once this is done we can use
a normal learning algorithm, such as the <a href="#svm_c_linear_trainer">svm_c_linear_trainer</a>,
on just the labeled data samples and obtain the same output as the manifold regularized
learner would have produced. Therefore, the linear_manifold_regularizer is
a tool for creating this preprocessing transformation. In particular, the
transformation is linear. That is, it is just a matrix you multiply with
all your samples.
</p>
<p>
For a more detailed discussion of this topic you should consult the following
paper. In particular, see section 4.2. This object computes the inverse T
matrix described in that section.
It turns out that it is possible to transform these manifold regularized loss
functions into the normal form shown above by applying a certain kind of
preprocessing to all our data samples. Once this is done we can use a
normal learning algorithm, such as the <a href="#svm_c_linear_trainer">svm_c_linear_trainer</a>,
on just the
labeled data samples and obtain the same output as the manifold regularized
learner would have produced.
</p>
<p>
The linear_manifold_regularizer is a tool for creating this preprocessing
transformation. In particular, the transformation is linear. That is, it
is just a matrix you multiply with all your samples. For a more detailed
discussion of this topic you should consult the following paper. In
particular, see section 4.2. This object computes the inverse T matrix
described in that section.
<blockquote>
Linear Manifold Regularization for Large Scale Semi-supervised Learning
by Vikas Sindhwani, Partha Niyogi, and Mikhail Belkin
</blockquote>
</p>
</description>
<examples>
<example>linear_manifold_regularizer_ex.cpp.html</example>
......
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