Artificial complex cells via the tropical semiring

The seminal work of Hubel and Wiesel [14] and the vast amount of work that followed it prove that hierarchies of increasingly complex cells play a central role in cortical computations. Computational models, pioneered by Fukushima [12], suggest that these hierarchies contain feature-building cells ("S-cells") and pooling cells ("C-cells"). More recently, Riesenhuber & Poggio have developed the HMAX model [25], in which S-cells perform linear combinations, while C-cells perform a MAX operation. We note that methods for computing the connectivity of S-cells abound since many algorithms for suggesting informative linear combinations exist. There are, however, only few published methods that are suitable for the construction of C-cells. Here, we build a novel dimensionality reduction algorithm for learning the connectivity of C-cells, using the framework of the max-plus ("tropical) semiring.