K-Regression Clustering for Interval-Valued Data

• Activity Number: 193
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Fei Liu* and Lynne Billard
• Companies: University of Georgia and University of Georgia
• Keywords: Symbolic data ; Interval-valued data ; K-regression ; clustering

Abstract

Symbolic data records are becoming a more powerful instrument to deal with large size data sets. Interval-valued data are a special type of symbolic data, for which each observation is a vector of intervals. The typical K-means methods for interval-valued data suppose the data separate to spherical clusters. It usually cannot converge to the correct clusters if the data are not clustering spherically. We propose a K-regression based clustering method for interval-valued data to recover a more complicated data structure. Assuming the response and predictor variables follow K different linear relationships, the data are initially split into K groups randomly. Then, we apply the new developed "symbolic variation" least squares to estimate the parameters of the K symbolic regressions. A data point is then relocated to its closest group in terms of its symbolic distance to the regression lines. This two-step dynamic clustering algorithm continues until the clusters are stable. Further, a plot of symbolic regression R-square versus the number of cluster K is used to determine the optimal number of clusters. The simulation shows that our method performs better than the K-means method.