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NeuroCOLT
Technical Report NC-TR-01-100
2001-100
Spectral
Kernel Methods for Clustering
Nello Christianini, John Shawe-Taylor, Jaz Kandola
ABSTRACT
In this paper we introduce new algorithms for unsupervised learning
based on the use of a kernel matrix. All the information required
by such algorithms is contained in the eigenvectors of the matrix
or of closely related matrices. We use two different but related cost
functions, the Alignment and the 'cut cost'. The first one is discussed
in a companion paper (3), the second one is based on graph theoretic
concepts. Both functions measure the level of clustering of a labeled
dataset, or the correlation between data clusters and labels. We state
the problem of unsupervised learning as assigning labels so as to
optimize these cost functions. We show how the optimal solution can
be approximated by slightly relaxing the corresponding optimization
problem, and how this corresponds to using eigenvector information.
The resulting simple algorithms are tested on real world data with
positive results.
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