A considerable body of findings on human face perception and computational methods of face identification has accumulated over the last years. One promising attempt to unify several phenomena reliably found in face perception research (e.g. the influence of distinctiveness on face perception; the other race effect) was proposed by Valentine (1991). He developed the idea of representing faces as points in a high-dimensional space, the dimensions of which would be capable of representing the perceived differences of faces. His approach has been used to predict and explain effects of distinctiveness, inversion and race in face recognition.

A further almost natural property to be expected of such a multidimensional space is the representation of similarity. The points in such a space may be grouped closely together or spaced apart and the different distances between points in face space should translate to different perceived similarities between the faces.

To be able to test whether this property actually holds for a face space, two things are necessary: the dimensions of face space have to be specified and perceived similarity of faces has to be measured. In the present work I examined a suitable model which specifies the dimensions of face space, and also tried to measure similarity with three different paradigms.

There seems to be a consensus that face spaces based on principal component analysis (PCA) of pixel values could be an interesting way to describe the early phases of human face perception. In this approach the variability between faces is captured by a purely statistical analysis of digitized images. This technique has been successfully applied in technical contexts, but it also has some merits as a psychological model: Several researchers were successful in describing aspects of human behavior using PCA-based models, for example classification by sex, the other-race effect, recognition of faces or judgements of distinctiveness.

A PCA of images proceeds as follows: Basically, a set of digitized images is collected under some constraints on size, position and illumination. These images can be considered as points in a very high-dimensional space, where each axis or dimension consists of one pixel. As long as we do not deal with random dot pictures, the set of images will only lie in a subspace of pixelspace. PCA now orthogonally rotates the original axes to efficiently represent the set of images at hand by successively explaining maximal variance between the images (in pixel coordinates). This results in new axes or dimensions of an image space which are ordered for “importance”, with axes of low order being more “important” than axes of higher order, if importance is understood as the amount of variance in the pictures explained by a specific dimension.

If this technique is applied to images of faces, the resulting new coordinate axes are usually named “eigenfaces”, since they are the eigenvectors of the pixel covariance matrix. Several researchers have been able to associate psychological variables with eigenfaces of low order but a simulation by O’Toole et al. (1993) also found important contributions of higher order dimensions for identification purposes. It seems as if variance captured by the first eigenfaces is due to general attributes like sex and race, with variance due to individuality of faces being represented in higher dimensions.

It is likely that several of these dimensions are taken into account when determining face similarity, but the actual number is not determined (at least by the PCA). Therefore the number of dimensions used in the computation of similarity as distance in face space has to be varied systematically. The comparison with empirical measures of similarity would then identify the specific face space out of the class of PCA-based face spaces which best predicts human similarity judgements.

Thus, one prerequisite for the goal of this study has been described: The method to identify the dimensions of face space will be PCA. The second problem is determination of (perceived) similarity of faces.

In contrast to other attributes of faces like attractiveness or distinctiveness there is no consensus on how to measure similarity of faces. Researchers working in the context of multidimensional scaling used direct rating procedures or sorting, but reaction time in discrimination tasks or probability of confusions have also been proposed. Laughery (1974) suggested false alarm rate in a recognition test as an indicator of similarity between groups of targets and distractors.

In a study which also examined PCA-based face spaces, Hancock et al. (1997) used a sorting procedure to measure similarity: Participants sorted 50 faces into piles according to similarity, with no restriction on the number of piles. Similarity ranks for pairs of faces were then derived from the number of times these faces co-occurred in the same pile. For each face, distances to the other faces in PCA-defined face space were computed and ranked in reverse order, such that large distances (indicating low similarity) resulted in low ranks. The authors report a small but significant mean rank correlation (rk=0.22) between similarity as measured by the sorting procedure and the inversely ranked distance measures in face space.