Visualization of High Dimensional Data in Brain and Information Sciences

Research field of my laboratory includes statistical mechanics especially for random magnetic systems, brain and information sciences. These three research areas share common mathematical structure. Their common feature is that they commonly treat very large freedom systems, that is, magnetism which originates from cooperative phenomena of O(1023) spins, brain functions carried by the large number of neuron activities, digital information represented by the large number of bit sequences. The statistical mechanics plays an important role to treat such large freedom systems because it can deduce macroscopic and low dimensional descriptions like the Boyle-Charle's law from microscopic and high dimensional descriptions of Newtonian or quantum mechanics. Since the statistical mechanics is considered as a systematic tool for the dimension reduction, it can be applicable to the brain and information systems. Since the dimension reduction is a common feature between the visualization and the statistical mechanics, the visualization also plays an important role to treat these systems. The visualization offers effective and essential low dimensional visual representations which help us to intuitively understand these systems. In this talk, I will present two examples regarding the visualization of high dimensional data in the brain and information sciences where the principal component analysis (PCA) and the mixture of Gaussian analysis (MGA) are employed. Sugase et al. performed single unit recordings in the inferior temporal (IT) cortex in the monkey's brain which is one of crucial areas regarding the pattern recognition. They presented 38 images to the monkey.