Constrained clusterwise linear regression

In market segmentation, Conjoint Analysis is often used to estimate the importance of a product attributes at the level of each single customer, clustering, successively, the customers whose behavior can be considered similar. The preference model parameter estimation is made considering data (usually opinions) of a single customer at a time, but these data are usually very few as each customer is called to express his opinion about a small number of different products (in order to simplify his/her work). In the present paper a Constrained Clusterwise Linear Regression algorithm is presented, that allows simultaneously to estimate parameters and to cluster customers, using, for the estimation, the data of all the customers with similar behavior.