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Jared Pincus, Jordan W Suchow; Estimating the dimensionality of face space empirically. Journal of Vision 2020;20(11):1456. doi: https://doi.org/10.1167/jov.20.11.1456.
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© ARVO (1962-2015); The Authors (2016-present)
Learned generative models of human identity and appearance, such as those that result from training deep neural networks on large databases of face photographs, are typically high-dimensional, representing each face as a point in a space with hundreds to thousands of dimensions. However, social perception of faces is low dimensional, relying on only a handful of key dimensions. What is the dimensionality of face space in the mind of an observer? To estimate the dimensionality, we begin with a simple observation: for any given person, there are many unrelated people who look similar to them. Consider, for example, the phenomena of "twin strangers" and "doppelgängers", where strangers look almost impossibly alike. Next, we note that the very concept of strong resemblance exists only in low dimensional spaces. When points are well-distributed in high dimensional spaces, nearest neighbors (i.e., a person and their closest doppelgänger) are nearly as far apart as randomly selected pairs of points (i.e., a person and a random stranger). By contradiction, face space must be low-dimensional. How low? Using the scaling relationship between dimensionality and nth-nearest-neighbor distances, it becomes possible to empirically estimate the dimensionality of face space by measuring the ratio of JNDs between random pairs of faces and faces paired with their nearest neighbors. In an experiment, we estimated this ratio empirically. To estimate the ratio, we first sampled a set of faces from a trained neural network (StyleGAN; Karras, Laine, & Aila, 2018). Next, we measured the distance between each pair of faces in JNDs through a psychophysical adjustment procedure. Finally, we computed the ratio of nearest-neighbor distances to random-neighbor distances. We found that the ratio, 0.76 [0.73, 0.79; 90% CI], implies a dimensionality of human face space between 7 and 12 dimensions.
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