Coding distributed representations of natural scenes: a comparison of orthogonal and non-orthogonal models

Abstract

Recent non-orthogonal models of simple cells (OF; Nature 381 (1996) 607) are based on the assumption that having desirable statistical properties (e.g., kurtosis) implies physiological plausibility. Orthogonal models which do not have certain statistical properties (e.g., equal variance distribution) have been dismissed without being tested under the same stimulus conditions as OF (localised segments of whitened natural scenes). In this paper, the statistical properties of OF are examined with respect to two alternatives: principal components analysis (PCA), which is the most parsimonious model, and independent components analysis (ICA), which directly optimises basis functions for kurtosis. After simulation on two different sets of whitened natural scenes (trees/plants with edges and short line segments and landscapes with less fine structure), it was found that the distribution of variance for trees/plants was similar for all three models. However, both ICA and PCA distributed variance more evenly than OF for landscapes, indicating an OF deficit in processing fine structure. Although OF was consistently more kurtotic than either ICA or PCA, OF must be substantially over-estimating the selectivity of its basis functions to process natural scenes, since ICA optimises this directly. These results demonstrate that (a) orthogonality is sometimes more appropriate for modelling neural responses than non-orthogonality; (b) OF and ICA are not formally equivalent; and (c) that desirable statistical distributions are highly sensitive to edges and short line segments. Are these distributions, therefore, the best criteria by which to judge the physiological plausibility of models of the visual cortex?