Algorithms for Representing Similarity Data
Abstract : This report develops and demonstrates algorithms for representing and displaying similarity data using three established cognitive models. The first representational model, multidimensional scaling, represents objects as points in a coordinate space so that similar objects lie near each other. The second representational model, the additive tree, represents objects as terminal nodes in a tree so that the similarity of two objects is modelled by length of the path between them. The third representational model, additive clustering, specifies a number of clusters with associated weights, so that the similarity of two objects is modelled by the sum of the weights of their common clusters. As well as listing and demonstrating MATLAB algorithms for finding these representations, a survey is presented of ways in which similarity and proximity data may be generated, and a principled Bayesian method of controlling the complexity of each representational model is presented. Finally, a number of suggestions are made regarding the use of the three representational models, and the relative strengths and weaknesses of the algorithms in relation to previously developed alternative algorithms are discussed.