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- T. Graepel, R. Herbrich,
P. Bollmann-Sdorra, and K. Obermayer. Classification on Pairwise Proximity
Data.
.
In Advances in Neural Information Processing Systems 11, pages
438-444, Cambridge, Massachusetts, 1999. MIT Press.
(FTP Gzipped PostScript, 7 pages, 65 kb)
We investigate the problem of learning a classification task on
data represented in terms of their pairwise proximities. This representation
does not refer to an explicit feature representation of the data items and is
thus more general than the standard approach of using Euclidean feature
vectors, from which pairwise proximities can always be calculated. Our first
approach is based on a combined linear embedding and classification procedure
resulting in an extension of the Optimal Hyperplane algorithm to
pseudo-Euclidean data. As an alternative we present another approach based on
a linear threshold model in the proximity values themselves, which is
optimized using Structural Risk Minimization. We show that prior knowledge
about the problem can be incorporated by the choice of distance measures and
examine different metrics w.r.t. their generalization. Finally, the
algorithms are successfully applied to protein structure data and to data
from the cats cerebral cortex. They show better performance than
K-nearest-neighbor classification.
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