Artificial Complex Cells via the Tropical Semiring

The seminal work of Hubel and Wiesel (1965) 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 (1980), suggest that these hierarchies contain feature-building cells ("S-cells") and pooling cells ("C-cells"). More recently, Riesenhuber & Poggio have developed the HMAX model (1999), 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.