运动中定位轨迹分析的高斯过程
Gaussian Processes for Analyzing Positioned Trajectories in Sports
摘要：
近年来，基于核的机器学习方法在探索和建模大数据集方面越来越受到关注。高斯过程（GP）是这种基于核的方法的一个例子，它可以为非线性建模问题提供非常好的性能。在这项工作中，我们首先提出了一个灰箱建模方法来分析越野滑雪比赛中的力量。更准确地说，一组有纪律的动力学运动模型公式与数据驱动的高斯过程回归模型相结合，该模型考虑了系统中的所有未知因素。然后，提出了一种建模方法来分析滑雪者的个人和集群的动力流。所提出的方法通常可以应用于定位轨迹和动力学测量可用的用例。所提出的方法进行了评估，使用收集的数据从法伦北欧世界滑雪锦标赛2015年，特别是男子越野$4\times10$公里接力。对越野滑雪比赛中的受力进行了分析和比较。速度模型的滑雪运动员在不同的比赛阶段进行了评估。最后，对灰箱法和黑箱法进行了比较，灰箱法可以将预测不确定度降低$30\%$到$40\%$。
英文摘要：
Kernel-based machine learning approaches are gaining increasing interest for exploring and modeling large dataset in recent years. Gaussian process (GP) is one example of such kernel-based approaches, which can provide very good performance for nonlinear modeling problems. In this work, we first propose a grey-box modeling approach to analyze the forces in cross country skiing races. To be more precise, a disciplined set of kinetic motion model formulae is combined with data-driven Gaussian process regression model, which accounts for everything unknown in the system. Then, a modeling approach is proposed to analyze the kinetic flow of both individual and clusters of skiers. The proposed approaches can be generally applied to use cases where positioned trajectories and kinetic measurements are available. The proposed approaches are evaluated using data collected from the Falun Nordic World Ski Championships 2015, in particular the Men's cross country $4\times10$ km relay. Forces during the cross country skiing races are analyzed and compared. Velocity models for skiers at different competition stages are also evaluated. Finally, the comparisons between the grey-box and black-box approach are carried out, where the grey-box approach can reduce the predictive uncertainty by $30\%$ to $40\%$.
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