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NeuroCOLT
Technical Report NC-TR-98-028
Quantization
Functionals and Regularized Principal Manifolds
Alex J. Smola
GMD
Sebastian Mika
GMD
Bernhard Schoelkopf
GMD
Received:
21-SEP-98
Abstract
Many settings of unsupervised learning can
be viewed as quantization problems, namely of minimizing the expected
quantization error subject to some restrictions. This has the advantage
that tools known from the theory of (supervised) risk minimization
like regularization can be readily applied to unsupervised settings.
Moreover, one may show that this setting is very closely related to
both, principal curves with a length constraint and the generative
topographic map. Experimental results demonstrate the feasibility
of the proposed method. In a companion paper we show that uniform
convergence bounds can be given for algorithms such as a modified
variant of the principal curves problem.
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