Generalizing Psychological Similarity Spaces to Unseen Stimuli

Generalizing Psychological Similarity Spaces to Unseen Stimuli Combining Multidimensional Scaling with Artificial Neural Networks Lucas Bechberger and Kai-Uwe Kühnberger Abstract The cognitive framework of conceptual spaces proposes to represent concepts as regions in psychological similarity spaces. These similarity spaces are typically obtained through multidimensional scaling (MDS), which converts human dissimilarity ratings for a fixed set of stimuli into a spatial representation. One can distinguish metric MDS (which assumes that the dissimilarity ratings are interval or ratio scaled) from nonmetric MDS (which only assumes an ordinal scale). In our first study, we show that despite its additional assumptions, metric MDS does not necessarily yield better solutions than nonmetric MDS. In this chapter, we furthermore propose to learn a mapping from raw stimuli into the similarity space using artificial neural networks (ANNs) in order to generalize the similarity space to unseen inputs. In our second study, we show that a linear regression from the activation vectors of a convolutional ANN to similarity spaces obtained by MDS can be successful and that the results are sensitive to the number of dimensions of the similarity space. 1 Introduction The cognitive framework of conceptual spaces [Gärdenfors, 2000] proposes a geometric representation of conceptual structures: Instances are represented as points and concepts are represented as regions in psychological similarity spaces. Based on this representation, one can explain a range of cognitive phenomena from oneshotLucas Bechberger Institute of Cognitive Science, Osnabrück University email: lucas.bechberger@ The research presented in this paper is an updated, corrected, and significantly extended version of research reported in [Bechberger and Kypridemou, 2018]. 1 arXiv:1908.09260v1 In principle, there are three ways of obtaining the dimensions of a conceptual space: If the domain of interest is well understood, one can manually define the dimensions and thus the overall similarity space. A second approach is based on machine learning algorithms for dimensionality reduction. For instance, unsupervised artificial neural networks (ANNs) such as autoencoders or self-organizing maps can be used to find a compressed representation for a given set of input stimuli. This task is typically solved by optimizing a mathematical error function which may be not satisfactory from a psychological point of view. A third way of obtaining the dimensions of a conceptual space is based on dissimilarity ratings obtained from human subjects. The technique of "multidimensional scaling" (MDS) takes as an input these pairwise dissimilarities as well as the desired number t of dimensions. It then represents each stimulus as a point in an t -dimensional space in such a way that the distances between points in this space reflect the dissimilarities of their corresponding stimuli.