Nonlinear time-series embedding by monotone variational inequality

TL;DR

This paper presents a novel convex optimization method based on monotone Variational Inequality for learning low-dimensional, faithful representations of nonlinear time series, with guarantees and applications in clustering and classification.

Contribution

It introduces a new, provably effective approach for unsupervised nonlinear time-series embedding using low-rank regularization and monotone Variational Inequality, applicable to diverse data types.

Findings

Competitive performance on real-world datasets

Effective for symbolic text modeling

Useful for RNA sequence clustering

Abstract

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.