  Time-series data is being increasingly collected and stud- ied in several
areas such as neuroscience, climate science, transportation, and social media.
Discovery of complex patterns of relationships between individual time-series,
using data-driven approaches can improve our understanding of real-world
systems. While traditional approaches typically study relationships between two
entire time series, many interesting relationships in real-world applications
exist in small sub-intervals of time while remaining absent or feeble during
other sub-intervals. In this paper, we define the notion of a sub-interval
relationship (SIR) to capture inter- actions between two time series that are
prominent only in certain sub-intervals of time. We propose a novel and
efficient approach to find most interesting SIR in a pair of time series. We
evaluate our proposed approach on two real-world datasets from climate science
and neuroscience domain and demonstrated the scalability and computational
efficiency of our proposed approach. We further evaluated our discovered SIRs
based on a randomization based procedure. Our results indicated the existence
of several such relationships that are statistically significant, some of which
were also found to have physical interpretation.
