# Topological Learning for Motion Data via Mixed Coordinates

arXiv: https://arxiv.org/abs/2310.19960 · HTML: https://mlsanity.com/paper/2310.19960/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 30 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 3 of 3)

- [Generalized Spectral Clustering via Gromov-Wasserstein Learning](https://mlsanity.com/paper/2006.04163/) (2020)
- [Multitask and Transfer Learning for Autotuning Exascale Applications](https://mlsanity.com/paper/1908.05792/) (2019)
- [Generalized Penalty for Circular Coordinate Representation](https://mlsanity.com/paper/2006.02554/) (2020)

## Abstract (arXiv)

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.