Fast string kernels using inexact matching for protein sequences

We describe several families of k-mer based string kernels related to the recently presented mismatch kernel and designed for use with support vector machines (SVMs) for classification of protein sequence data. These new kernels - restricted gappy kernels, substitution kernels, and wildcard kernels - are based on feature spaces indexed by k-length subsequences ("k-mers") from the string alphabet Σ. However, for all kernels we define here, the kernel value K(x,y) can be computed in O(c_K(|x| + |y|)) time, where the constant c_K depends on the parameters of the kernel but is independent of the size |Σ| of the alphabet. Thus the computation of these kernels is linear in the length of the sequences, like the mismatch kernel, but we improve upon the parameter-dependent constant c_K = k^m+1|Σ|^m of the (k,m)-mismatch kernel. We compute the kernels efficiently using a trie data structure and relate our new kernels to the recently described transducer formalism. In protein classification experiments on two benchmark SCOP data sets, we show that our new faster kernels achieve SVM classification performance comparable to the mismatch kernel and the Fisher kernel derived from profile hidden Markov models, and we investigate the dependence of the kernels on parameter choice.