Complex and Object Data
Increasingly in many “modern” application areas, it has become common to collect data that have a structure that is not well represented by a simple scalar, vector or matrix. For example, for each subject under study, one may observe a curve over time, a complex shape or even a multiway array or graph. Such object data cannot be analyzed using traditional statistical methods, and new approaches need to be designed that appropriately characterize the geometry of the data, while enabling statistical inferences. The development of such methods is inherently inter-disciplinary. Defining appropriate mathematical representations of the data which do not overly simplify the geometric and topological structure requires knowledge of functional analysis. Developing models and methodology for fitting these models to data and performing inferences requires substantial statistical skills. In addition, computation and data processing and storage are often daunting, requiring adeptness with design of efficient algorithms and skills in computer science. Fortunately, Duke is particularly inter-disciplinary with faculty who are experts in each of these complementary areas of “geometric data science”.