GRM: Generalized regression model for clustering linear sequences

Linear relation is valuable in rule discovery of stocks, such as "if stock X goes up 1, stock Y will go down 3", etc. The traditional linear regression models the linear relation of two sequences perfectly. However, if user asks "please cluster the stocks in the NASDAQ market into groups where sequences have strong linear relationship with each other", it is prohibitively expensive to compare sequences one by one. In this paper, we propose a new model named GRM (Generalized Regression Model) to gracefully handle the problem of linear sequences clustering. GRM gives a measure, GR ², to tell the degree of linearity of multiple sequences without having to compare each pair of them. Our experiments on the stocks in the NASDAQ market mined out many interesting clusters of linear stocks accurately and efficiently using the GRM clustering algorithm.