Efficient Geometric-based Computation of the String Subsequence Kernel

Kernel methods are powerful tools in machine learning. They have to be computationally efficient. In this paper, we present a novel Geometric-based approach to compute efficiently the string subsequence kernel (SSK). Our main idea is that the SSK computation reduces to range query problem. We started by the construction of a match list $L(s,t)=\{(i,j):s_{i}=t_{j}\}$ where $s$ and $t$ are the strings to be compared; such match list contains only the required data that contribute to the result. To compute efficiently the SSK, we extended the layered range tree data structure to a layered range sum tree, a range-aggregation data structure. The whole process takes $O(p|L|\log|L|)$ time and $O(|L|\log|L|)$ space, where $|L|$ is the size of the match list and $p$ is the length of the SSK. We present empiric evaluations of our approach against the dynamic and the sparse programming approaches both on synthetically generated data and on newswire article data. Such experiments show the efficiency of our approach for large alphabet size except for very short strings. Moreover, compared to the sparse dynamic approach, the proposed approach outperforms absolutely for long strings.