GaKCo: a Fast GApped k-mer string Kernel using COunting

String Kernel (SK) techniques, especially those using gapped k-mers as features (gk), have obtained great success in classifying sequences like DNA, protein, and text. However, the state-of-the-art gk-SK runs extremely slow when we increase the dictionary size ({Sigma}) or allow more mismatches (M). This is because current gk-SK uses a trie-based algorithm to calculate co-occurrence of mismatched substrings resulting in a time cost proportional to O({Sigma}M). We propose a fast algorithm for calculating Gapped k-mer Kernel using Counting (GaKCo). GaKCo uses associative arrays to calculate the co-occurrence of substrings using cumulative counting. This algorithm is fast, scalable to larger{Sigma} and M, and naturally parallelizable. We provide a rigorous asymptotic analysis that compares GaKCo with the state-of-the-art gk-SK. Theoretically, the time cost of GaKCo is independent of the{Sigma} M term that slows down the trie-based approach. Experimentally, we observe that GaKCo achieves the same accuracy as the state-of-the-art and outperforms its speed by factors of 2, 100, and 4, on classifying sequences of DNA (5 datasets), protein (12 datasets), and character-based English text (2 datasets). 1