On Compact Codes for Spatially Pooled Features

Feature encoding with an overcomplete dictionary has demonstrated good performance in many applications, especially computer vision. In this paper we analyze the classification accuracy with respect to dictionary size by linking the encoding stage to kernel methods and \nystrom sampling, and obtain useful bounds on accuracy as a function of size. The \nystrom method also inspires us to revisit dictionary learning from local patches, and we propose to learn the dictionary in an end-to-end fashion taking into account pooling, a common computational layer in vision. We validate our contribution by showing how the derived bounds are able to explain the observed behavior of multiple datasets, and show that the pooling aware method efficiently reduces the dictionary size by a factor of two for a given accuracy.