Statistical Models for Querying and Managing Time-Series Data

In recent years we are experiencing a dramatic increase in the amount of available time-series data. Primary sources of time-series data are sensor networks, medical monitoring, financial applications, news feeds and social networking applications. Availability of large amount of time-series data calls for scalable data management techniques that enable efficient querying and analysis of such data in real-time and archival settings. Often the time-series data generated from sensors (environmental, RFID, GPS, etc.), are imprecise and uncertain in nature. Thus, it is necessary to characterize this uncertainty for producing clean answers. In this thesis we propose methods that address these important issues pertaining to time-series data. Particularly, this thesis is centered around the following three topics: Computing Statistical Measures on Large Time-Series Datasets. Computing statistical measures for large databases of time series is a fundamental primitive for querying and mining time-series data [31, 81, 97, 111, 132, 137]. This primitive is gaining importance with the increasing number and rapid growth of time-series databases. In Chapter 3, we introduce the Affinity framework for efficient computation of statistical measures by exploiting the concept of affine relationships [113, 114]. Affine relationships can be used to infer a large number of statistical measures for time series, from other related time series, instead of computing them directly; thus, reducing the overall computational cost significantly. Moreover, the Affinity framework proposes an unified approach for computing several statistical measures at once. Creating Probabilistic Databases from Imprecise Data. A large amount of time-series data produced in the real-world has an inherent element of uncertainty, arising due to the various sources of imprecision affecting its sources (like, sensor data, GPS trajectories, environmental monitoring data, etc.). The primary sources of imprecision in such data are: imprecise sensors, limited communication bandwidth, sensor failures, etc. Recently there has been an exponential rise in the number of such imprecise sensors, which has led to an explosion of imprecise data. Standard database techniques cannot be used to provide clean and consistent answers in such scenarios. Therefore, probabilistic databases that factor-in the inherent uncertainty and produce clean answers are required. An important assumption i while using probabilistic databases is that each data point has a probability distribution associated with it. This is not true in practice — the distributions are absent. As a solution to this fundamental limitation, in Chapter 4 we propose methods for inferring such probability distributions and using them for efficiently creating probabilistic databases [116]. Managing Participatory Sensing Data. Community-driven participatory sensing is a rapidly evolving paradigm in mobile geo-sensor networks. Here, sensors of various sorts (e.g., multi-sensor units monitoring air quality, cell phones, thermal watches, thermometers in vehicles, etc.) are carried by the community (public vehicles, private vehicles, or individuals) during their daily activities, collecting various types of data about their surrounding. Data generated by these devices is in large quantity, and geographically and temporally skewed. Therefore, it is important that systems designed for managing such data should be aware of these unique data characteristics. In Chapter 5, we propose the ConDense (Community-driven Sensing of the Environment) framework for managing and querying community-sensed data [5, 19, 115]. ConDense exploits spatial smoothness of environmental parameters (like, ambient pollution [5] or radiation [2]) to construct statistical models of the data. Since the number of constructed models is significantly smaller than the original data, we show that using our approach leads to dramatic increase in query processing efficiency [19, 115] and significantly reduces memory usage.

A FFINITY: Efficiently Querying Statistical Measures on Time-Series Data

Karl Aberer, Saket Sathe

Computing statistical measures for large databases of time series is a fundamental primitive for querying and mining time-series data [1]–[6]. This primitive is gaining importance with the increasing number and rapid growth of time series databases. In this paper, we introduce a framework for efficient computation of statistical measures by exploiting the concept of affine relationships. Affine relationships can be used to infer statistical measures for time series, from other related time series, instead of computing them directly; thus, reducing the overall computational cost significantly. The resulting methods exhibit at least one order of magnitude improvement over the best known methods. To the best of our knowledge, this is the first work that presents an unified approach for computing and querying several statistical measures at once. Our approach exploits affine relationships using three key components. First, the AFCLST algorithm clusters the time-series data, such that high-quality affine relationships could be easily found. Second, the SYMEX algorithm uses the clustered time series and efficiently computes the desired affine relationships. Third, the SCAPE index structure produces a many-fold im- provement in the performance of processing several statistical queries by seamlessly indexing the affine relationships. Finally, we establish the effectiveness of our approaches by performing comprehensive experimental evaluation on real datasets.

IEEE2013

Fast Correlation Discovery for Large-Scale Streaming Time-Series Data

Karl Aberer, Tian Guo, Saket Sathe

The dramatic rise of streaming time-series data produced in a vari- ety of contexts, such as stock markets, mobile sensing, sensor net- works, data centre monitoring, etc., has fuelled the development of large-scale distributed real-time computation systems ( e.g., Apache Storm, Spark Streaming, S4, etc.). However, it is still unclear how certain important tasks, which can be performed with relative ease in a centralized system, could be performed using such distributed systems. In this paper, we focus on one such task of continu- ously discovering correlations among a large number of stream- ing time series. While doing so, we address two key challenges: (1) the number of time-series pairs that have to be analyzed grows quadratically (O(n2)) in the number of time-series n, giving rise to a quadratic increase in the communication cost between differ- ent nodes of the distributed system, (2) as the size of the time series grows, the computational and communication costs again increase at a prohibitive rate. To tackle these challenges, we propose an approach referred to as AEGIS. AEGIS approximates a group of streams using afﬁne trans- formations. Then it only communicates these stream groups, which are smaller in size and therefore signiﬁcantly reduces the communi- cation overhead. Secondly, AEGIS dramatically enhances the com- putational efﬁciency by exploiting the properties of afﬁne transfor- mations to prune the number of evaluated correlations. As for base- lines we adapt well-known centralized correlation computation ap- proaches to the distributed environment. Our extensive experimen- tal evaluations on real and synthetic datasets establish that AEGIS outperforms the baseline approaches in terms of communication cost, processing latency, and peak capacity.

2014