Renewing the respect for similarity

Abstract

In psychology, the concept of similarity has traditionally evoked a mixture of respect, stemming from its ubiquity and intuitive appeal, and concern, due to its dependence on the framing of the problem at hand and on its context. We argue for a renewed focus on similarity as an explanatory concept, by surveying established results and new developments in the theory and methods of similarity-preserving associative lookup and dimensionality reduction—critical components of many cognitive functions, as well as of intelligent data management in computer vision. We focus in particular on the growing family of algorithms that support associative memory by performing hashing that respects local similarity, and on the uses of similarity in representing structured objects and scenes. Insofar as these similarity-based ideas and methods are useful in cognitive modeling and in AI applications, they should be included in the core conceptual toolkit of computational neuroscience. In support of this stance, the present paper (1) offers a discussion of conceptual, mathematical, computational, and empirical aspects of similarity, as applied to the problems of visual object and scene representation, recognition, and interpretation, (2) mentions some key computational problems arising in attempts to put similarity to use, along with their possible solutions, (3) briefly states a previously developed similarity-based framework for visual object representation, the Chorus of Prototypes, along with the empirical support it enjoys, (4) presents new mathematical insights into the effectiveness of this framework, derived from its relationship to locality-sensitive hashing (LSH) and to concomitant statistics, (5) introduces a new model, the Chorus of Relational Descriptors (ChoRD), that extends this framework to scene representation and interpretation, (6) describes its implementation and testing, and finally (7) suggests possible directions in which the present research program can be extended in the future