An evaluation of two algorithms for hierarchical classes analysis

The family of hierarchical classes models is a distinctive collection of di rect two-sided clustering models for two-way two-mode binary data. In the a ssociated data analysis, a data matrix D is approximated by a binary matrix M that can be represented by a hierarchical classes model of a prespecifie d rank k. In this procedure, a least-squares loss function in terms of disc repancies between D and R I is minimized. The present paper describes the o riginal hierarchical classes algorithm proposed by De Boeck and Rosenberg ( 1988), which is based on an alternating greedy heuristic, and proposes a ne w algorithm, based on an alternating branch-and-bound procedure. An extensi ve simulation study is reported in which both algorithms are evaluated and compared according to goodness-of-fit to the data and goodness-of-recovery of the underlying true structure. Furthermore, three heuristics for selecti ng models of different ranks for a given D are presented and compared. The simulation results show that the new algorithm yields models with slightly higher goodness-of-fit and goodness-of-recovery values.