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Linear-time algorithms for the subpath kernel

Authors Kilho Shin, Taichi Ishikawa

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Author Details

Kilho Shin
  • Graduate School of Applied Informatics, University of Hyogo, Minatojima-Minamimachi, Chuo, Kobe, Japan
Taichi Ishikawa
  • Graduate School of Applied Informatics, University of Hyogo, Minatojima-Minamimachi, Chuo, Kobe, Japan

Funding

  • Shin, Kilho: This work was supported by JSPS KAKENHI Grant Number JP17H007623 and JP16K12491.

Cite As Get BibTex

Kilho Shin and Taichi Ishikawa. Linear-time algorithms for the subpath kernel. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 22:1-22:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CPM.2018.22

Abstract

The subpath kernel is a useful positive definite kernel, which takes arbitrary rooted trees as input, no matter whether they are ordered or unordered, We first show that the subpath kernel can exhibit excellent classification performance in combination with SVM through an intensive experiment. Secondly, we develop a theory of irreducible trees, and then, using it as a rigid mathematical basis, reconstruct a bottom-up linear-time algorithm for the subtree kernel, which is a correction of an algorithm well-known in the literature. Thirdly, we show a novel top-down algorithm, with which we can realize a linear-time parallel-computing algorithm to compute the subpath kernel.

Subject Classification

ACM Subject Classification
  • Theory of computation → Kernel methods
Keywords
  • tree
  • kernel
  • suffix tree

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