A Framework for Space-Efficient String Kernels

Abstract

String kernels are typically used to compare genome-scale sequences whose length makes alignment impractical, yet their computation is based on data structures that are either space-inefficient, or incur large slowdowns. We show that a number of exact string kernels, like the \(k\)-mer kernel, the substrings kernels, a number of length-weighted kernels, the minimal absent words kernel, and kernels with Markovian corrections, can all be computed in \(O(nd)\) time and in \(o(n)\) bits of space in addition to the input, using just a \(\mathtt {rangeDistinct}\) data structure on the Burrows-Wheeler transform of the input strings that takes \(O(d)\) time per element in its output. The same bounds hold for a number of measures of compositional complexity based on multiple values of \(k\), like the \(k\)-mer profile and the \(k\)-th order empirical entropy, and for calibrating the value of \(k\) using the data.