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arXiv · 2310.19960

Topological Learning for Motion Data via Mixed Coordinates

Hengrui Luo·Jisu Kim·Alice Patania·Mikael Vejdemo-Johansson
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Abstract

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.

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Hengrui Luo, Jisu Kim, Alice Patania, Mikael Vejdemo-Johansson. 2023-10-30. Topological Learning for Motion Data via Mixed Coordinates. https://doi.org/10.1109/bigdata52589.2021.9671525

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