Principles of Multi-kernel Data Mining

Abstract

The scientific community has accumulated an immense experience in processing data represented in finite-dimensional linear spaces of numerical features of entities, whereas the kit of mathematical instruments for dissimilarity-based processing of data in metric spaces representing distances between entities, for which sufficiently informative features cannot be found, is much poorer. In this work, the problem of embedding the given set of entities into a linear space with inner product by choosing an appropriate kernel function is considered as the major challenge in the featureless approach to estimating dependences in data sets of arbitrary kind. As a rule, several kernels may be heuristically suggested within the bounds of the same data analysis problem. We treat several kernels on a set of entities as Cartesian product of the respective number of linear spaces, each supplied with a specific kernel function as a specific inner product. The main requirement here is to avoid discrete selection in eliminating redundant kernels with the purpose of achieving acceptable computational complexity of the fusion algorithm.

This work is supported by the Russian Foundation for Basic Research (Grants 02-01-00107 and 05-01-00679), Grant of the President of the Russian Federation for young scientists No. MK-3173.2004.09 (O. Seredin), INTAS Grant 04-77-7347, and NSF Grant CCR 0325398 (I. Muchnik).