Representing Complex Shapes with Conceptual Spaces

Lucas Bechberger, Margit Scheibel

Keywords: Shapes, Conceptual Spaces, Multidimensional Scaling

Abstract:

Shape representations play a central role in our interaction with the world [1]. Nevertheless, we have only a vague understanding of how shape knowledge is represented.
In this paper, we use the framework of conceptual spaces [2] as a modeling tool for representing complex shapes. In this framework, each object is represented as a point in the conceptual space whose coordinates represent the object specific values of the employed quality dimensions. The geometric distance between two points represents the similarity between two objects (the smaller the distance, the more similar the objects). Higher-order concepts can be identified as convex, non-overlapping regions.
Our study aims at discovering structural characteristics of a shape space that can explain human perception and categorizations of complex shapes. This can contribute to new insights and a deeper understanding of perceptual processes but also allows for constructive uses, e.g. in the context of cognitive AI.
Based on human similarity ratings for pictures of common objects, shape spaces of varying dimensionality were constructed and validated by considering how well the similarities are reflected in the distances. Moreover, the conceptual regions for example categories were analyzed. In a second analysis step, we tested whether primitive shape features are detectable as quality dimensions in the shape spaces. The analysis scripts used in our study are available at https://github.com/lbechberger/LearningPsychologicalSpaces.