Data analysis for high-dimensional data with discrete structures and its applications

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The main goal of this research is to develop methodologies for efficient searches of solutions with global optimality or for incorporating discrete structures as prior knowledge in combinatorial analyses with high-dimensional data. Moreover, we aim at its evaluation of the usefulness in applications where combinatorial computation plays a central role. We developed some fundamental algorithms to calculate global/approximate optimal solutions in problems that are known to be difficult to solve(such as, NP-hard problems). Also, we studied a framework for the calculation where we can incorporate such discrete structures as prior knowledge into data analysis for efficient and accurate combinatorial calculation. Furthermore, we applied the developed methods to several applications and investigate the usefulness of the framework.