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Nakamura Laboratory (Graduate School of Information Science, University of Hyogo)
Nonlinear Data Analysis: Revealing the Underlying Nature of Phenomena from Data  (The world we see and know is not all there is)

The Nakamura Laboratory studies the characteristics of phenomena that vary irregularly and seeks to uncover the underlying mechanisms behind them through data. For me, the starting point of data analysis lies in freely imagining features or nature within data that no one has yet noticed. This way of thinking is also what drives the development of new analytical methods. Data analysis is a branch of applied mathematics in which data obtained from various phenomena in the real world are analysed mathematically and statistically using knowledge, experience and computers.

Examples of phenomena that vary irregularly include fluctuations in electric current, changes in temperature, exchange rate and DNA sequences. Such phenomena are found across a wide range of fields, including biology, society, meteorology, economics, seismology and astrophysics, and in many cases the underlying mechanisms are not yet fully understood. It may also be difficult to investigate the phenomena themselves directly or in detail while preserving their natural state. For this reason, it is important to observe a phenomenon and use the resulting data to investigate its characteristics and underlying mechanisms. Data may contain a wealth of information about the phenomenon — or at least we hope that they do — but the data themselves are merely collections of numbers or symbols. Only by identifying regularities and structures within them and interpreting these as meaningful information can we begin to understand the phenomenon itself.

It is known that irregular and complex behaviour can arise from factors such as interactions among multiple variables, time delays (periodicities), and nonlinearity. Another important factor is nonstationarity, in which the system that generates a phenomenon, or the parameters governing that system, changes over time. These features or nature are not easy to deal with appropriately, but they are essential to understanding complex phenomena. In the Nakamura laboratory, we aim to reveal features or nature within the data and to uncover the mechanisms behind them while taking account of multiple variables and their interactions, time delays (periodicities,) nonlinearity, and nonstationarity. We also develop new analytical methods required for this purpose. Such perspectives and methods have the potential to be applied across a broad range of fields, from the natural sciences to social phenomena.

Whenever possible, I would like to pursue research for which there is no model or precedent to follow — research that discovers a door no one has noticed before and then opens it. I believe that different ways of thinking lead to different outcomes, and that new ways of thinking give rise to new ideas and discoveries. In this sense, the “data analysis” that I pursue may be regarded as a kind of philosophical exploration using mathematics, computers and data. Through this research, we aim to develop the ability to understand complex phenomena mathematically and to uncover their essential nature from data.

My main research approaches are as follows:

Research keywords: time series analysis, statistical modelling, dynamical systems, nonlinear phenomena, optimisation problems