Topological Learning for Motion Data via Mixed Coordinates
This work addresses a specific bottleneck in transfer learning for time and motion series, offering an incremental improvement by integrating topological clustering into kernel design.
The paper tackles the challenge of constructing effective functional kernels for multiple output Gaussian processes in time series analysis by incorporating topological information through a novel mixed valued coordinates framework, resulting in a unified approach for motion data.
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.