Topological Learning for Motion Data via Mixed Coordinates
Hengrui Luo Jisu Kim Alice Patania Mikael Vejdemo-Johansson
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.