Linear grouping using orthogonal regression

This paper proposes a new method, called linear grouping algorithm (LGA), to detect different linear structures in a data set. LGA is useful for investigating potential linear patterns in datasets, that is, subsets that follow different linear relationships. LGA combines ideas from principal components, clustering methods and resampling algorithms. It can detect several different linear relations at once. We also propose methods to determine the number of groups in the data and diagnostic tools to investigate the results obtained from LGA. It is shown how LGA can be extended to detect groups characterized by lower dimensional hyperplanes as well. Some applications illustrate the usefulness of LGA in practice.