Introducing Novel Relationships in Time Series Data

Abstract

In many scientific and engineering domains such as climate, neuroscience, transportation, etc. measurements are collected from sensors installed in different parts of a complex dynamical system over regular intervals of time, resulting in a collection of large volumes of time series data. Automated data-driven approaches that can mine relationships between different time series could potentially lead to discovery of previously unknown physical processes which could further aid in designing policies and solutions to critical problems such as climate change, severe mental disorders, traffic congestion etc. This thesis defines novel relationships and patterns that can be studied in the time series data. In particular, the proposed definitions can capture two new types of relationships: i) multivariate relationships involving more than two time series, and ii) sub-interval relationships, that only exist during certain sub-intervals of time and are absent or occur very feebly during rest of the time. The other major contributions of this thesis include designing new automated data-driven approaches to find most interesting instances of defined relationships from the data in a computationally efficient manner, and proposing empirical approaches to assess the statistical significance of obtained relationships. The proposed approaches were applied to real-world datasets from two scientific domains: i) climate, and ii) neuroscience, and led to discovery of several new instances of relationships. Many of these instances are found to be statistically significant and reproducible in multiple time series datasets that are independent of the original dataset. One such instance led to the discovery of a climate phenomenon that was previously unknown to climate scientists.