Nonlinear time-series embedding by monotone variational inequality
This work addresses the challenge of representing complex sequential data for downstream tasks like clustering and classification, but it is incremental as it builds on existing autoregressive and low-rank regularization techniques.
The paper tackles the problem of unsupervised learning of low-dimensional representations for nonlinear time series, such as electrocardiograms and natural language, by introducing a method based on monotone variational inequality with low-rank regularization, achieving competitive performance on real-world data like symbolic text modeling and RNA sequence clustering.
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.