Mathematical Foundations Modeled after Neo-Cortex for Discovery and Understanding of Structures in Data
Even though there are distinct areas for different functionalities in the mammalian neo-cortex, it seems to use the same algorithm to understand a large variety of input modalities. In addition, it appears that the neo-cortex effortlessly identifies the correlation among many sensor modalities and fuses information obtained from them. The question then is, can we discover the brain’s learning algorithm and approximate it for problems such as computer vision and automatic speech recognition that the mammalian brain is so good at? The answer is: it is an orders of magnitude problem, i.e., not a simple task. However, we can attempt to develop mathematical foundations based on the understanding of how a human brain learns. This chapter is focused along that direction. In particular, it is focused on the ventral stream – the “what pathway” - and describes common algorithms that can be used for representation and classification of signals from different sensor modalities such as auditory and visual. These common algorithms are based on dictionary learning with a beta process, hierarchical graphical models, and embedded hidden Markov models.