MATH178 HM - Nonlinear Data Analytics

Credit(s): 3

Instructor(s): Gu

Offered: Fall

Description: Analysis of nonlinear large dynamic data including but not limited from automobiles, cell phones, robots, and unmanned aerial vehicles (UAVs). Visualization of such data using geometric methods, followed by representation 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.) Advanced geometric data analysis techniques including nonlinear Riemannian (non-Euclidean) distances for modeling such big data problems (as used for building a cost function). We will also demonstrate how to perform optimization techniques on curved configuration spaces by extending optimization methods such as gradient descent and Newton’s method to such curved spaces. Application of learned techniques to solve real world problems involving big nonlinear dynamic data.

Prerequisite(s): CSCI070 HM and (CSCI140 HM or MATH131 HM or MATH157 HM or MATH168 HM)