Sunday, October 02, 2005

Discrete SVMs

I think that there is the possibility of defining discrete Support Vector Machines.
It's unfortunate that all SVM theory as I read it assumes that the codomain of the kernel function
is the Eucludean space. Although the theory will often say that the input space can be any countable set, the examples and implementations seem to assume too often that you got R as your input space. And why not use a free module instead of a vector space? It seems to me that all of this can be generalized to allow for discrete spaces. That would be interesting! Maybe someone in the future will be able to define the musical structures in algebraic terms, or using a topology, and then allow a machine to operate directly on the music pieces. Not allowing the use of discrete spaces for me restricts the applicability of the SVM theory to other inputs that are countable in ways other than the field of the reals.

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