One of my researches is the construction of the theory and methodology of high-dimensional data analysis. In recent years, our current interests are in the field of Big Data such as genetic microarrays, medical imaging, text recognition, finance, chemometrics, and so on. From now on, the utilization of such data will be required more than ever.
A characteristic of Big Data is a huge number of dimensions. In particular, it is difficult in the case of High-Dimensional Small-Sample-Size, where the dimensions is much larger than sample size. For example, the microarray data has tens of thousands to millions of genes, but we have only a few tens of samples.
We assume that the number of samples is sufficiently larger than the number of dimensions in the conventional statistics so that it cannot be analyzed by using it as it is. Occasionally, traditional statistics have various problems in high-dimensional small-sample-size data analysis due to the curse of dimensionality.
Aoshima Lab has proposed methods by using a geometric representation of data space in high-dimensional and the dual space. At Shimodaira Lab, we are working on mathematical analysis of machine learning and are actively researching deep learning.