Abstract:

The aim of this paper is to develop an algorithm for solving the clusterwise
linear least absolute deviations regression problem. This problem is formulated as a
nonsmooth nonconvex optimization problem, and the objective function is represented
as a difference of convex functions. Optimality conditions are derived by using this
representation. An algorithm is designed based on the difference of convex representation
and an incremental approach. The proposed algorithm is tested using small to
large artificial and real-world data sets.

Key words: Clusterwise regression ·, Nonsmooth optimization ·, Smoothing ·
Incremental algorithm