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.

翻译：拓扑学能够高效地提取数据集中的结构信息。本文尝试将拓扑信息融入多输出高斯过程模型，以实现迁移学习。为此，我们扩展了圆形坐标框架，提出了一种混合值坐标新框架，以考虑时间序列中的线性趋势。利用多输出高斯过程模型有效学习多个时间序列的主要挑战之一是构建函数核。我们提出采用拓扑诱导聚类，在多输出高斯过程模型中构建基于聚类的核函数。该核不仅整合了拓扑结构信息，还使我们能够提出一个统一框架，用于在时间和运动序列中利用拓扑信息。