Topological Learning for Motion Data via Mixed Coordinates

• URL: http://arxiv.org/abs/2310.19960v1
• Date: Mon, 30 Oct 2023 19:20:48 GMT
• Title: Topological Learning for Motion Data via Mixed Coordinates
• Abstract summary: Topology can extract structural information in a dataset efficiently. We propose to incorporate topological information into a multiple output Gaussian process model. We put forward a unified framework using topological information in time and motion series.
• Score: 2.5955102874701517
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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