LINEAR AND CIRCULAR UNIDIMENSIONAL SCALING FOR SYMMETRICAL PROXIMITY MATRICES

The tasks of linear and circular unidimensional scaling can be charact erized by the attempt to represent the entries in a symmetric proximit y matrix through distances among a set of object locations defined eit her along a linear continuum or around a closed, circular continuum. T hese two scaling tasks are approached through a least-squares optimiza tion strategy based on a combination of combinatorial search and itera tive projection techniques. Extensions are provided for considering mu ltiple linear or circular unidimensional structures, and to the inclus ion of several representational alternatives offered by (restricted) a dditive tree models. Two published data sets are used to illustrate th e results obtainable from the optimization method being proposed.