Linear and circular unidimensional scaling for symmetric proximity matrices
Lawrence J. Hubert, Phipps Arabie, Jacqueline J. Meulman · British Journal of Mathematical and Statistical Psychology · 1997
The tasks of linear and circular unidimensional scaling can be characterized by the attempt to represent the entries in a symmetric proximity matrix through distances among a set of object locations defined either along a linear continuum or around a closed, circular continuum. These two scaling tasks are approached through a least‐squares optimization strategy based on a combination of combinatorial search and iterative projection techniques. Extensions are provided for considering multiple linear or circular unidimensional structures, and to the inclusion of several representational alternatives offered by (restricted) additive tree models. Two published data sets are used to illustrate the results obtainable from the optimization method being proposed.