Course Description

In this course, we will cover analysis of nonlinear large dynamic data including but not limited from auto cars, cell phones, robots, and unmanned aerial vehicles (UAVs). We will start with visualizing such data using geometric methods. We then will represent such data in certain configuration spaces to capture the intrinsic non-linear relationship in the data. (For example, UAVs’ data including accelerometer and gyroscope data, obeys nonlinear kinematics and dynamics relationships, a curved 3-D sphere S3 can capture their rotations when we use unit quaternion representations. A traditional statistical correlation matrix cannot capture those nonlinear relations since a correlation matrix only captures linear relationships in the data.) We will then cover more advanced geometric data analysis techniques including nonlinear Riemannian (non-Euclidean) distances for modeling such big data problems (e.g. used for building a cost function). We will also demonstrate how to perform optimization techniques on such curved configuration spaces by extending optimization methods such as gradient descent and Newton’s method to such curved spaces. Finally, we will apply our learned techniques to solve real-world problems involving big nonlinear dynamic data.

Summary of Goals

  • Gain a comprehensive view of nonlinear data analytics as an academic discipline and understand the mathematics behind it.

  • Be able to search and read recent academic papers in the nonlinear data analytics literature and apply those algorithms and concepts to real world problems.

  • Become comfortable with industry and academia standard tools (such as AWS and GitHub) and be able to find and work with large, public datasets.