Persistence - Based Data Analysis and Classification

The main goals of the project are the formalization and the development of a novel approach to the analysis, comparison and classification of multidimensional data, i.e. information characterized by features embedded in some multidimensional topological space. Our proposed project will be based on a topological exploration and understanding of data, finding its roots in the so-called (multidimensional) persistence, a theoretical and computational methodology recently emerged as a suitable tool for such purposes. The framework developed within the project does not aim to replace existing data analysis tools. It will provide a new tool enabling the use of additional information, hence improving the existing frameworks, making them more robust and stable. One further contribution will be the finding of important data properties with regard to the multidimensional persistence framework.