In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of time series that have strong linear dependence among themselves, with the requirement that each time series makes a significant contribution to the linear dependence. We demonstrate that most interesting multipoles can be identified as cliques of negative correlations in a correlation network. Such cliques are typically rare in a real-world correlation network, which allows us to find almost all multipoles efficiently using a clique-enumeration approach. Using our proposed framework, we demonstrate the utility of multipoles in discovering new physical phenomena in two scientific domains: climate science and neuroscience. In particular, we discovered several multipole relationships that are reproducible in multiple other independent datasets and lead to novel domain insights.

Mining relationships in time series data is of immense interest to several disciplines such as neuroscience, climate science, and transportation. Traditional approaches for mining relationships focus on discovering pair-wise relationships in the data. In this work, we define a novel relationship pattern involving three interacting time series, which we refer to as a tripole. We show that tripoles capture interesting relationship patterns in the data that are not possible to be captured using traditionally studied pair-wise relationships. We demonstrate the utility of tripoles in multiple real-world datasets from various domains including climate science and neuroscience. In particular, our approach is able to discover tripoles that are statistically significant, reproducible across multiple independent data sets, and lead to novel domain insights.

Statistical modeling of local precipitation involves understanding local, regional and global factors informative of precipitation variability in a region. Modern machine learning methods for feature selection can potentially be explored for identifying statistically significant features from pool of potential predictors of precipitation. In this work, we consider sparse regression, which simultaneously performs feature selection and regression, followed by random permutation tests for selecting dominant factors. We consider average winter precipitation over Great Lakes Region in order to identify its dominant influencing factors.Experiments show that global climate indices, computed at different temporal lags, offer predictive information for winter precipitation. Further, among the dominant factors identified using randomized permutation tests, multiple climate indices indicate the influence of geopotential height patterns on winter precipitation.Using composite analysis, we illustrate that certain patterns are indeed typical in high and low precipitation years, and offer plausible scientific reasons for variations in precipitation.Thus, feature selection methods can be useful in identifying influential climate processes and variables, and thereby provide useful hypotheses over physical mechanisms affecting local precipitation.

Swirls of ocean currents known as ocean eddies are a crucial component of the ocean's dynamics. In addition to dominating the ocean's kinetic energy, eddies play a significant role in the transport of water, salt, heat, and nutrients. Therefore, understanding current and future eddy patterns is a central climate challenge to address future sustainability of marine ecosystems. The emergence of sea surface height observations from satellite radar altimeter has recently enabled researchers to track eddies at a global scale. The majority of studies that identify eddies from observational data employ highly parametrized connected component algorithms using expert filtered data, effectively making reproducibility and scalability challenging. In this paper, we frame the challenge of monitoring ocean eddies as an unsupervised learning problem. We present a novel change detection algorithm that automatically identifies and monitors eddies in sea surface height data based on heuristics derived from basic eddy properties. Our method is accurate, efficient, and scalable. To demonstrate its performance we analyze eddy activity in the Nordic Sea (60-80N and 20W-20E), an area that has received limited attention and has proven to be difficult to analyze using other methods.

Dipoles represent long distance connections between the pressure anomalies of two distant regions that are negatively correlated with each other. Such dipoles have proven important for understanding and explaining the variability in climate in many regions of the world, e.g., the El Nino climate phenomenon is known to be responsible for precipitation and temperature anomalies over large parts of the world. Systematic approaches for dipole detection generate a large number of candidate dipoles, but there exists no method to evaluate the significance of the candidate teleconnections. In this paper, we present a novel method for testing the statistical significance of the class of spatio-temporal teleconnection patterns called as dipoles. One of the most important challenges in addressing significance testing in a spatio-temporal context is how to address the spatial and temporal dependencies that show up as high autocorrelation. We present a novel approach that uses the wild bootstrap to capture the spatio-temporal dependencies, in the special use case of teleconnections in climate data. Our approach to find the statistical significance takes into account the autocorrelation, the seasonality and the trend in the time series over a period of time. This framework is applicable to other problems in spatio-temporal data mining to assess the significance of the patterns.

Droughts are one of the most damaging climate-related hazards. The late 1960s Sahel drought in Africa and the North American Dust Bowl of the 1930s are two examples of severe droughts that have an impact on society and the environment. Due to the importance of understanding droughts, we consider the problem of their detection based on gridded datasets of precipitation. We formulate the problem as the one of finding the most likely configuration of a Markov Random Field and propose an efficient inference algorithm. We apply this algorithm to the Climate Research Unit precipitation dataset spanning 106 years. The empirical results show that the algorithm successfully identifies the major droughts of the twentieth century in different regions of the world.

Given a spatiotemporal (ST) dataset and a path in its embedding spatiotemporal framework, the goal is to to identify all interesting sub-paths defined by an interest measure. Sub-path discovery is of fundamental importance for understanding climate changes, agriculture, and many other application. However, this problem is computationally challenging due to the massive volume of data, the varying length of sub-paths and non-monotonicity of interestingness throughout a sub-path. Previous approaches find interesting unit sub-paths (e.g., unit time interval) or interesting points. By contrast, we propose a Sub-path Enumeration and Pruning (SEP) approach that finds collections of long interesting sub-paths. Two case studies using climate change datasets show that SEP can find long interesting sub-paths which represent abrupt climate change. We provide theoretical analyses of correctness, completeness and computational complexity of the proposed approach. We also provide experimental evaluation of two traversal strategies for enumerating and pruning candidate sub-paths.