Discovering the Whole by the Coarse: A topological paradigm for data analysis

The increasing interest in big data applications is ushering in a large effort in seeking new, efficient, and adapted data models to reduce complexity, while preserving maximal intrinsic information. Graph-based models have recently been getting a lot of attention on account of their intuitive and direct connection to the data [43]. The cost of these models, however, is to some extent giving up geometric insight as well as algebraic flexibility.