Human demonstrations of trajectories are an important source of training data for many machine learning problems. However, the difficulty of collecting human demonstration data for complex tasks makes learning efficient representations of those trajectories challenging. For many problems, such as for handwriting or for quasistatic dexterous manipulation, the exact timings of the trajectories should be factored from their spatial path characteristics. In this work, we propose TimewarpVAE, a fully differentiable manifold-learning algorithm that incorporates Dynamic Time Warping (DTW) to simultaneously learn both timing variations and latent factors of spatial variation. We show how the TimewarpVAE algorithm learns appropriate time alignments and meaningful representations of spatial variations in small handwriting and fork manipulation datasets. Our results have lower spatial reconstruction test error than baseline approaches and the learned low-dimensional representations can be used to efficiently generate semantically meaningful novel trajectories.

翻译：人类演示的轨迹数据是许多机器学习问题的重要训练来源。然而，针对复杂任务收集人类演示数据的困难性使得学习这些轨迹的有效表示充满挑战。对于许多问题，例如手写或准静态灵巧操作，轨迹的精确时序应与其空间路径特征分离开来。本文提出TimewarpVAE，一种全微分流形学习算法，该算法融合动态时间规整（DTW）以同时学习时序变化和空间变化的潜在因子。我们展示了TimewarpVAE算法如何在小型手写数据集和叉子操作数据集中学习适当的时间对齐以及有意义的空间变化表示。相较于基线方法，我们的结果在空间重构测试误差方面更低，且学习到的低维表示可用于高效生成语义新颖的轨迹。