The Mapping Distance – a Generalization of the Edit Distance – and its Application to Trees

Kilho Shin, Taro Niiyama

2018

Abstract

The edit distances has been widely used as an effective method to analyze similarity of compound data, which consist of multiple components, such as strings, trees and graphs. For example, the Levenshtein distance for strings is known to be effective to analyze DNA and proteins, and the Ta¨ı distance and its variations are attracting wide attention of researchers who study tree-type data such as glycan, HTML-DOM-trees, parse trees of natural language processing and so on. The problem that we recognize here is that the way of engineering new edit distances was ad-hoc and lacked a unified view. To solve the problem, we introduce the concept of the mapping distance. The mapping distance framework can provide a unified view over various distance measures for compound data focusing on partial one-to-one mappings between data. These partial one-to-one mappings are a generalization of what are known as traces in the legacy study of edit distances. This is a clear contrast to the legacy edit distance framework, which define distances between compound data through edit operations and edit paths. Our framework enables us to design new distance measures consistently, and also, various distance measures can be described using a small number of parameters. In fact, in this paper, we take rooted trees as an example and introduce three independent dimensions to parameterize mapping distance measures. As a result, we define 16 mapping distance measures, 13 of which are novel. In experiments, we discover that some novel measures outperform the others including the legacy edit distances in accuracy when used with the k-NN classifier.

Paper Citation

in Harvard Style

Shin K. and Niiyama T. (2018). The Mapping Distance – a Generalization of the Edit Distance – and its Application to Trees.In Proceedings of the 10th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-275-2, pages 266-275. DOI: 10.5220/0006721902660275

in Bibtex Style

@conference{icaart18,
author={Kilho Shin and Taro Niiyama},
title={The Mapping Distance – a Generalization of the Edit Distance – and its Application to Trees},
booktitle={Proceedings of the 10th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2018},
pages={266-275},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006721902660275},
isbn={978-989-758-275-2},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - The Mapping Distance – a Generalization of the Edit Distance – and its Application to Trees
SN - 978-989-758-275-2
AU - Shin K.
AU - Niiyama T.
PY - 2018
SP - 266
EP - 275
DO - 10.5220/0006721902660275