Abstract
Following earlier studies which showed that a sparse coding principle may explain the receptive field properties of complex cells in primary visual cortex, it has been concluded that the same properties may be equally derived from a slowness principle. In contrast to this claim, we here show that slowness and sparsity drive the representations towards substantially different receptive field properties. To do so, we present complete sets of basis functions learned with slow subspace analysis (SSA) in case of natural movies as well as translations, rotations, and scalings of natural images. SSA directly parallels independent subspace analysis (ISA) with the only difference that SSA maximizes slowness instead of sparsity. We find a large discrepancy between the filter shapes learned with SSA and ISA. We argue that SSA can be understood as a generalization of the Fourier transform where the power spectrum corresponds to the maximally slow subspace energies in SSA. Finally, we investigate the trade-off between slowness and sparseness when combined in one objective function.
Highlights
The appearance of objects in an image can change dramatically depending on their pose, distance, and illumination
The invariance of complex cell responses in primary visual cortex against small translations is commonly interpreted as a signature of an invariant coding strategy possibly originating from an unsupervised learning principle
Various models have been proposed to explain the response properties of complex cells using a sparsity or a slowness criterion and it has been concluded that physiologically plausible receptive field properties can be derived from either criterion
Summary
The appearance of objects in an image can change dramatically depending on their pose, distance, and illumination. Learning representations that are invariant against such appearance changes can be viewed as an important preprocessing step which removes distracting variance from a data set in order to improve performance of downstream classifiers or regression estimators [1]. It is an inherent part of training a classifier to make its response invariant against all within-class variations. Rather than learning these invariances for each object class individually, we observe that many transformations such as translation, rotation and scaling apply to any object independent of its specific shape This suggests that signatures of such transformations exist in the spatio-temporal statistics of natural images which allow one to learn invariant representations in an unsupervised way. A variety of neural algorithms have been proposed that aim at explaining the response properties of complex cells as components of an invariant representation that is optimized for the spatio-temporal statistics of the visual input [4,5,6,7,8,9,10,11,12]
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