Capstone Address
Chair: Issei Fujishiro 
14:0015:15, March 7, 2008. 
Visualization of High Dimensional Data in Brain and Information Sciences 
Masato Okada 
The University of Tokyo and RIKEN Brain Science Institute 
Abstract 
The research field of my laboratory includes statistical mechanics
especially for random magnetic systems, brain and information sciences.
These three research areas share a common mathematical structure.
Their common feature is that they commonly treat very large freedom
systems, that is, magnetism that originates from cooperative phenomena
of O(1023) spins, that brain functions are carried by a large number of
neuron activities, that digital information is represented by a large
number of bit sequences. The statistical mechanics plays an important
role in treating such large freedom systems because it can be used to
deduce macroscopic and low dimensional descriptions like the BoyleCharle's
law from microscopic and high dimensional descriptions of Newtonian or
quantum mechanics. Because the statistical mechanics is considered to be
a systematic tool for the dimension reduction, it is applicable to brain
and information systems. The dimension reduction is a common feature between
the visualization and the statistical mechanics, so the visualization also
plays an important role in treating these systems. The visualization offers
effective and essential low dimensional visual representations that help us
to understand these systems intuitively. In this presentation, I will
present two examples regarding the visualization of high dimensional data
in brain and information sciences where principal component analysis (PCA)
and mixture of Gaussian analysis (MGA) are used.
Sugase et al. presented 38 images to two monkeys and conducted single unit recordings in the inferior temporal (IT) cortex, a crucial area for pattern recognition. The 38 images were divided into three groups: a group with monkey faces, a group with human faces, and a group with simple shapes. The group with human faces was further divided into three individual human faces with four facial expressions. The group with monkey faces was further divided into four individual monkey faces with four facial expressions. There is a hierarchical structure in the set of images. In this presentation, I will visualize how this hierarchical structure is encoded in the neuronal population in the IT cortex. We picked up 45 neurons that were recorded and calculated the temporal evolutions of their neural firing rates. We thus mapped the 38 images to 38 neural population vectors in a 45 dimensional space. We visualized temporal evolutions of the 38 neural population vectors using the PCA and a clustering based on the MGA to explore the neural information representation of the hierarchical structure in the set of images. We found that the neural population vectors split into three clusters corresponding to human faces, monkey faces and other simple shapes in the early phase (90140msec), and that these three clusters split into subclusters corresponding to finer categorizations in the later phase (140190msec). This finding strongly suggests that the hierarchical structure embedded in the set of images is encoded in the temporal evolutions of neuron activities in the IT cortex. Next I will show the visualization of the lowdensity paritycheck (LDPC) code using the same technique as an example in the information science. The LDPC is of great interest because it saturates the Shannon's bound. We numerically obtained the posterior distribution of transmitted bits using a Markov chain Monte Carlo (MCMC) method and extracted the first and second principal components (PC) by using the covariance matrix of the MCMC simulation. The static and dynamic properties of the LDPC are visualized and could be discussed intuitively on the two dimensional space spanned by two PCs.

Biography 
Masato Okada received a B.Sc. degree in physics from Osaka City University in 1985 and, an M.Sc. degree in physics and a Ph.D. degree in science from Osaka University in 1987 and 1997. From 1987 to 1989, he worked at Mitsubishi Electric Corporation. From 1989 to 1991, he was a student of the Graduate School of Engineering Science, Osaka University, and from 1991 to 1996 he was a research associate at Osaka University. From 1996 to 2001, he was a researcher in the Kawato Dynamic Brain Project, JST. From 2001 to 2004, he was a deputy laboratory head in the laboratory for mathematical neuroscience, RIKEN Brain Science Institute and a researcher of intelligent cooperation and control, PRESTO, JST from 2002 to 2004. Since 2004, he is a professor at the department of complexity science and engineering, the Graduate School of Frontier Science, the University of Tokyo. 