Topological Learning for Motion Data via Mixed Coordinates
- Resource Type
- Conference
- Authors
- Luo, Hengrui; Kim, Jisu; Patania, Alice; Vejdemo-Johansson, Mikael
- Source
- 2021 IEEE International Conference on Big Data (Big Data) Big Data (Big Data), 2021 IEEE International Conference on. :3853-3859 Dec, 2021
- Subject
- Communication, Networking and Broadcast Technologies
Computing and Processing
Power, Energy and Industry Applications
Robotics and Control Systems
Signal Processing and Analysis
Measurement
Adaptation models
Transfer learning
Time series analysis
Gaussian processes
Big Data
Market research
Topological data analysis
persistent cohomology
multiple-output Gaussian process
metric learning
- Language
Topology can extract the structural information in a dataset efficiently. In this paper, we attempt to incorporate topological information into a multiple output Gaussian process model for transfer learning purposes. To achieve this goal, we extend the framework of circular coordinates into a novel framework of mixed valued coordinates to take linear trends in the time series into consideration.One of the major challenges to learn from multiple time series effectively via a multiple output Gaussian process model is constructing a functional kernel. We propose to use topologically induced clustering to construct a cluster based kernel in a multiple output Gaussian process model. This kernel not only incorporates the topological structural information, but also allows us to put forward a unified framework using topological information in time and motion series.