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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.
References
[3] Nello Cristianini, André Elisseeff, John
Shawe-Taylor, and Jaz Kandola. On kernel target alignment.
Submitted to
Proceedings of Neural Information Processing Systems
(NIPS), 2001.
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