Predicting Similarity Ratings to Faces using Physical Descriptions
A perceptually-grounded, nonmetric feature mapping model is introduced. This model explicitly relates similarity ratings from a facial comparison experiment to various primitive, physically derived facial features such as Gabor jets, principal components and geometric features. In this approach, abstract features are formed that combine and weight information from the primitive facial features. The abstract features form the basis for predicting the similarity ratings for faces. We show how this model extracts abstract "age" and "facial adiposity" features on the basis of all similarity ratings to 50 faces. Whereas traditional multidimensional scaling methods can also uncover important variables for face perception, this model has the additional advantage of making explicit how to compute these variables from primitive facial features. Another advantage of this approach is that the featural descriptions can be used in a generalization test to predict similarity ratings to new faces. We show how this generalization test enables us to constrain various parameters of the model such as the dimensionality of the representation. Introduction A major goal in the field of face perception is to determine appropriate representations and processes operating on these representations. Faces are enormously, and perhaps infinitely complex (Townsend, Solomon, & SpencerSmith, this volume). By the same token, they all share a recognizable shape and configuration: for example, the nose is always between the mouth and the eyes. Although faces consist of a high number of dimensions, the representation of faces may be thought of as a compression or mapping of the featural dimensions into a lower-dimensional space by either ignoring some dimensions or reducing the redundancies among dimensions. Face perception may be thought of as a process by which the physical features of faces are combined in order to support recognition or categorization tasks. To capture the representations that are used in face perception, researchers have adopted one of two major approaches. The purely psychological and top-down approach In the purely psychological approach based on multidimensional representations (e.g. Ashby, 1992; Nosofsky 1986, 1991, 1992), a face is represented abstractly as a point in a multidimensional space (Valentine, 1991a, b; this volume). The positions of the points can be derived from data from various psychological tasks with Scaling techniques such as Multidimensional Scaling (MDS) (Kruskal 1964a,b; Shepard 1962a,b, 1974, 1980; Torgeson 1952). In nonmetric MDS, the goal is to find a configuration of points in some multidimensional space such that the interpoint distances are monotonically related to the experimentally obtained dissimilarities. The dissimilarities can be derived from similarity judgements, dissimilarity judgments, confusion matrices, reaction times from discrimination Predicting Similarity Ratings 2 experiments, correlation coefficients or any other measure of pairwise proximity. In metric MDS, the goal is to find a configuration of points and an appropriate function that transforms the interpoint distances such that the transformed distances match the experimental dissimilarities exactly. In the Appendix, we give a short introduction to nonmetric MDS. Several researchers using MDS analyses on faces (Busey, this volume, 1998; Johnston, Milne & Williams, 1997; Shepard, Ellis, & Davies, 1977) have developed multidimensional "face-space" representations: the faces are located in a multidimensional space such that similar faces are located in similar regions and that the pairwise distances between the facelocations reflect their perceived similarity. Busey (this volume; 1998) has applied MDS to similarity ratings on all pairs of a set of 100 faces. Based on a six dimensional configuration, the dimensions were interpreted as age, race, facial adiposity, facial hair, aspect ratio of head and color of facial hair. The goal of Busey’s work was to predict recognition performance with various computational models that took the configuration of points as a basis for representing the faces. The resulting MDS solutions for the configuration of points in low-dimensional spaces can give valuable insights about the way faces are perceived, and sometimes forms a useful basis for modeling performance in recognition and/or categorization tasks. Although the resultant dimensions are sometimes given a featural interpretation, this approach explicitly ignores the physical representation of the features comprising the faces. In this purely top-down approach, the multidimensional representations are sometimes difficult to relate back to the physical stimulus. The purely computational and bottom-up