Geometric Models of Similarity

Abstract: This dissertation examines and discusses some phenomena related to the geometric representation of similarity. It takes its inspiration from the existing body of empirical research within the fields of perceptual and cognitive psychology, but also connects to certain areas of machine learning. The problems discussed concern the modelling of information integration behavior when concepts like asymmetry, integrality, separability and familiarity are taken into account. The dissertation investigates how these phenomena can be modelled using geometric representations in order to increase the descriptive power of the models. The main conclusions that can be drawn from this dissertation are that the descriptive powers of geometric models can be increased in a number of ways: a) By augmenting traditional geometric models with parameters of prominence they can reflect asymmetric similarity at least as well as previously known asymmetric models which include more parameters. b) Some specific metric, for instance, the Euclidean metric, should not be used merely by tradition. If there is reason to believe that there are groupings of dimensions such that the most descriptive metric differs between groups, the distance may be better described with a combination rule adding the contribution of each group/subspace together. c) Aspects of familiarity with stimuli should be taken into consideration, even for familiarity built up during a short period of time. When taking familiarity into consideration it may be possible to describe information integration over time with a finer granularity. Furthermore, by focusing on the part of the phenomenological data that reflect a more stable behavior, which seems to occur first when subjects are sufficiently familiar with the stimuli, the more stable behavior can be more accurately described.