Large volumes of spatio-temporal data are increasingly collected and studied in diverse domains, including climate science, social sciences, neuroscience, epidemiology, transportation, mobile health, and Earth sciences. Spatio-temporal data differ from relational data for which computational approaches are developed in the data-mining community for multiple decades in that both spatial and temporal attributes are available in addition to the actual measurements/attributes. The presence of these attributes introduces additional challenges that needs to be dealt with. Approaches for mining spatio-temporal data have been studied for over a decade in the data-mining community. In this article, we present a broad survey of this relatively young field of spatio-temporal data mining. We discuss different types of spatio-temporal data and the relevant data-mining questions that arise in the context of analyzing each of these datasets. Based on the nature of the data-mining problem studied, we classify literature on spatio-temporal data mining into six major categories: clustering, predictive learning, change detection, frequent pattern mining, anomaly detection, and relationship mining. We discuss the various forms of spatio-temporal data-mining problems in each of these categories. There are a few recent surveys that have reviewed the literature on STDM in certain contexts from different perspectives. Articles by Vatsavai et al. (2012) and Chandola et al. (2015) discuss the computational issues for STDM algorithms in the era of "big-data" for application domains such as remote sensing, climate science, and social media analysis. The review by covers STDM approaches for prediction, clustering, and visualization problems in several applications. An extensive survey of approaches for mining trajectory data, one of the many types of ST data, is presented in Li (2014), Zheng (2015) , and Mamoulis (2009). A survey on STDM by provides a semantic categorization of ST data types and pattern families from a database-centric perspective. Given the richness of problems and the variety of methods being explored in the rapidly advancing field of STDM, there is a need for developing an over-arching structure of research in STDM that highlights the similarities and differences of different problems and methods in diverse ST applications. This can enable the cross-pollination of ideas across disparate research areas and application domains by making it possible to see how a solution developed for a certain problem in a particular domain (e.g., identifying patterns in climate data) can be useful for solving a different problem in another domain (e.g., understanding the working of the brain). This can also help in connecting the traditional data-mining community with the challenges and opportunities in analyzing ST data, thus exposing some of the open questions and motivating future directions of research in STDM. This review article on STDM problems and methods attempts to fulfill this need as follows. First, it builds a foundation of ST data types and properties that can help in identifying the relevant problems and methods for any class of ST data encountered in real-world applications. In particular, we provide a broad taxonomy of the different types of ST data, different ways of defining and describing ST data instances, and different ways of computing similarity among ST data instances. Second, it presents a survey of STDM approaches for a number of commonly studied data-mining problems such as clustering, predictive learning, frequent pattern mining, anomaly detection, change detection, and relationship mining. For every category of problems, we review the novel issues that arise in dealing with the unique properties of ST data types in classical datamining frameworks. This article can be used as a guide by data-mining researchers and real-world practitioners working with ST data to identify STDM formulations fit for their data and to make most effective use of STDM research in their problem. In addition, by bridging the gap between classical data-mining literature and the novel aspects of spatio-temporal data, this article helps in opening novel possibilities of future research. The rest of the article is organized as follows. In Section 2, we review the variety of application areas where analyzing ST data is important. In Section 3, we discuss the types and characteristics of ST data, and the different ways of defining instances and similarity measures using ST data types. Section 4 presents a survey of STDM methods developed for different types of ST data instances in the context of six major data-mining problems, viz., clustering, predictive learning, frequent pattern mining, anomaly detection, change detection, and relationship mining. Section 5 presents concluding remarks and discusses future research directions. Large volumes of ST data are collected in several application domains such as social media, healthcare, agriculture, transportation, and climate science. In this section, we briefly describe the different sources of ST data and the motivation for analyzing ST data in different application domains. Climate Science: Data pertaining to historic and current atmospheric and oceanic conditions (e.g., temperature, pressure, wind-flow, and humidity) is collected and studied in climate science 83:4 G. Atluri et al. (Karpatne et al. 2013 ). In addition to observational data 1 collected from weather stations and reanalysis data that is gridded in space (Kistler et al. 2001) , simulated data generated using climate models (Voldoire et al. 2013) is also studied in this domain. The purpose in studying this data is to discover relationships and patterns in climate science that advance our understanding of the Earth's system and help us better prepare for future adverse conditions by informing adaptation and mitigation actions in a timely manner. Neuroscience: Continuous neural activity captured using a variety of technologies such as Functional Magnetic Resonance Imaging (fMRI), Electroencephalogram (EEG), and Magnetoencephalography (MEG) is studied in neuroscience (Atluri et al. 2016) . Spatial resolution of neural activity measured using these technologies is quite different from another. For example, neural activity is measured from millions of locations in fMRI data, while it is only measured from tens of locations in the case of EEG data. Temporal resolution of the data collected using these technologies is also quite different. For example, fMRI typically measures activity for every 2s, while the temporal resolution of EEG data is is typically 1ms. The purpose in studying these data is to understand the governing principles of the brain and thereby determine the disruptions to normal conditions that arise in the case of mental disorders (Atluri et al. 2013 (Atluri et al. , 2015 . Discovering such disruptions can be useful for designing diagnostic procedures and in developing therapeutic procedures for patients. Environmental Science: Studying the data pertaining to the quality of air, water, and environment is one of the objectives of environmental science. While air quality is measured based on the presence of pollutants such as particles, carbon monoxide, nitrogen dioxide, sulphur dioxide, ozone, and so on, water quality is measured based on factors such as dissolved oxygen, conductivity, turbidity, and pH. Air quality sensors are typically placed on streets or on top of buildings, and water quality sensors are placed in lakes, rivers, and streams. In addition to air and water quality, data pertaining to sound pollution is also collected. These environmental datasets are studied to detect changes in levels of pollution, identify the causal factors that contribute to pollution, and design effective policies to reduce the different types of pollution (Thompson et al. 2014) . Precision Agriculture: Multi-band high-resolution (ranging from 0.25m to 1m) areal or remote-sensing images of large farms are being collected at regular intervals (e.g., daily to weekly). One of the purposes of collecting and studying these data is to detect plant diseases (Mahlein 2016) and understand the impact of several factors such as misapplication of fertilizer, compaction during planting and weeds on crop yield, as well as their inter-relationships. With the help of this knowledge, steps can be taken in future crop cycles to mitigate the risks due to the factors that adversely affect the crop yield. Epidemiology/Health care: Electronic health record data that are widely stored in hospitals provide demographic information pertaining to patients as well diagnoses made on patients at different time points. This dataset can be represented as a spatio-temporal dataset where each diagnosis has a spatial location and a time-point associated with it. One can construct such spatiotemporal instances for different types of diseases such as cancers and diabetes, as well as for infectious diseases such as influenza. These data are studied to discover spatio-temporal patterns in different diseases (Matsubara et al. 2014 ) and to study the spread of an epidemic. These data are also used in conjunction with environmental, climate science datasets to discover relationships between environmental factors and public health (Ryan et al. 2007) . Discovery of such relationships will allow policy-makers to develop effective policies that will ensure the well-being of the population.
A recent review of the emerging field of spatio-temporal data mining highlights the importance of anomaly detection techniques for the dynamic networks domain REF .
Spatio-Temporal Data Mining: A Survey of Problems and Methods
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