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- J. Hochreiter
and K. Obermayer. Support Vector Machines for Dyadic Data.
.
Neural Comput., 18:1472-1510, 2006.
(FTP PDF, 416 kb)
We describe a new technique for the analysis of dyadic data, where
two sets of objects ("row" and "column" objects) are
characterized by a matrix of numerical values which describe their mutual
relationships. The new technique, called "Potential Support Vector
Machine" (P-SVM), is a large-margin method for the construction of
classifiers and regression functions for the "column" objects.
Contrary to standard support vector machine approaches, the P-SVM minimizes a
scale-invariant capacity measure and requires a new set of constraints. As a
result, the P-SVM method leads to a usually sparse expansion of the
classification and regression functions in terms of the "row"
rather than the "column" objects and can handle data and kernel
matrices which are neither positive definite nor square. We then describe two
complementary regularization schemes. The first scheme improves
generalization performance for classification and regression tasks, the
second scheme leads to the selection of a small, informative set of
"row" "support" objects and can be applied to feature
selection. Benchmarks for classification, regression, and feature selection
tasks are performed with toy data as well as with several real world data
sets. The results show, that the new method is at least competitive with but
often performs better than the benchmarked standard methods for standard
vectorial as well as for true dyadic data sets. In addition, a theoretical
justification is provided for the new approach.
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