Partition of Interval-Valued Observations Using Regression

Both regression modeling and clustering methodologies have been extensively studied as separate techniques. There has been some activity in using regression-based algorithms to partition a data set into clusters for classical data; we propose one such algorithm to cluster interval-valued data. The new algorithm is based on the k-means algorithm of MacQueen (1967) and the dynamical partitioning method of Diday and Simon (1976), with the partitioning criteria being based on establishing regression models for each sub-cluster. This also depends on distance measures between the underlying regression models for each sub-cluster. Several types of simulated data sets are generated for several different data structures. The proposed k-regressions algorithm consistently out-performs the k-means algorithm. Elbow plots are used to identify the total number of clusters K in the partition. The new method is also applied to real data.