In the wild, we often encounter collections of sequential data such as
electrocardiograms, motion capture, genomes, and natural language, and
sequences may be multichannel or symbolic with nonlinear dynamics. We introduce
a new method to learn low-dimensional representations of nonlinear time series
without supervision and can have provable recovery guarantees. The learned
representation can be used for downstream machine-learning tasks such as
clustering and classification. The method is based on the assumption that the
observed sequences arise from a common domain, but each sequence obeys its own
autoregressive models that are related to each other through low-rank
regularization. We cast the problem as a computationally efficient convex
matrix parameter recovery problem using monotone Variational Inequality and
encode the common domain assumption via low-rank constraint across the learned
representations, which can learn the geometry for the entire domain as well as
faithful representations for the dynamics of each individual sequence using the
domain information in totality. We show the competitive performance of our
method on real-world time-series data with the baselines and demonstrate its
effectiveness for symbolic text modeling and RNA sequence clustering.

通过无监督学习非线性时间序列的低维表示方法，该方法基于每个序列服从自身的自回归模型并通过低秩约束与其他序列相关联的假设，可以用于聚类和分类等机器学习任务，并且在真实时间序列数据上展示了有竞争力的性能和符号文本建模和 RNA 序列聚类的有效性。