A Study on the Clustering Algorithms for Line Segments

• Activity Number: 176 - Contributed Poster Presentations: Section on Statistics and the Environment
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Yoshitomo Akimoto* and Toshinari Kamakura
• Companies: Chuo University and Chuo University
• Keywords: Circular data ; Angular data ; Clustering ; k-means ; LM test ; line segment

Abstract

Directional data have been studied as one of the major statistical topics in the field of spacial analysis sometimes must handle directional objects in 2-dimentional space. As the applications of directional statistics, we will investigate the angles of line segments such as line faults closely related with earthquake. We cannot define the start and the end points on the line segments. Angular data are periodic and the range is basically (0, 2pi), but the range of the line segment without direction is (0, pi). It is a good idea to summarize angular data of line segments by estimating distribution of data and their clusters. In this article we propose a method of clustering such data. As a devising method for angular data, we derivate the new test statistics called LM test for two samples. LM test statistics are calculated by score statistics using Lagrange multiplier. We investigate the performance of this test statistics. We also propose the clustering method for angular data in addition to test statistics. Finally, numerical simulations are provided to demonstrate the performances of the new clustering algorithms.