To monitor critical infrastructure, high quality sensors sampled at a high frequency are increasingly installed. However, due to the big amounts of data produced, only simple aggregates are stored. This removes outliers and hides fluctuations that could indicate problems. As a solution we propose compressing time series with dimensions using a model-based method we name Multi-model Group Compression (MMGC). MMGC adaptively compresses groups of correlated time series with dimensions using an extensible set of models within a user-defined error bound (possibly zero). To partition time series into groups, we propose a set of primitives for efficiently describing correlation for data sets of varying sizes. We also propose efficient query processing algorithms for executing multi-dimensional aggregate queries on models instead of data points. Last, we provide an open-source implementation of our methods as extensions to the model-based Time Series Management System (TSMS) ModelarDB. ModelarDB interfaces with the stock versions of Apache Spark and Apache Cassandra and thus can reuse existing infrastructure. Through an evaluation we show that, compared to widely used systems, our extended ModelarDB provides up to 11 times faster ingestion due to high compression, 65 times better compression due to the adaptivity of MMGC, 92 times faster aggregate queries as they are executed on models, and close to linear scalability while also being extensible and supporting online query processing.
We summarize papers about model-based time series management and model-based olap . These are surveys about model-based time series management @cite_3 @cite_12 , Hadoop olap @cite_22 and tsms @cite_2 .
@cite_22 @cite_12 @cite_3 @cite_2
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The collection of time series data increases as more monitoring and automation are being deployed. These deployments range in scale from an Internet of things (IoT) device located in a household to enormous distributed Cyber-Physical Systems (CPSs) producing large volumes of data at high velocity. To store and analyze these vast amounts of data, specialized Time Series Management Systems (TSMSs) have been developed to overcome the limitations of general purpose Database Management Systems (DBMSs) for times series management. In this paper, we present a thorough analysis and classification of TSMSs developed through academic or industrial research and documented through publications. Our classification is organized into categories based on the architectures observed during our analysis. In addition, we provide an overview of each system with a focus on the motivational use case that drove the development of the system, the functionality for storage and querying of time series a system implements, the components the system is composed of, and the capabilities of each system with regard to Stream Processing and Approximate Query Processing (AQP) . Last, we provide a summary of research directions proposed by other researchers in the field and present our vision for a next generation TSMS. Time series data mining has received much greater interest along with the increase in temporal data sets from different domains such as medicine, finance, multimedia, etc. Representations are important to reduce dimensionality and generate useful similarity measures. High-level representations such as Fourier transforms, wavelets, piecewise polynomial models, etc., were considered previously. Recently, autoregressive kernels were introduced to reflect the similarity of the time series. We introduce a novel approach to model the dependency structure in time series that generalizes the concept of autoregression to local autopatterns. Our approach generates a pattern-based representation along with a similarity measure called learned pattern similarity (LPS). A tree-based ensemble-learning strategy that is fast and insensitive to parameter settings is the basis for the approach. Then, a robust similarity measure based on the learned patterns is presented. This unsupervised approach to represent and measure the similarity between time series generally applies to a number of data mining tasks (e.g., clustering, anomaly detection, classification). Furthermore, an embedded learning of the representation avoids pre-defined features and an extraction step which is common in some feature-based approaches. The method generalizes in a straightforward manner to multivariate time series. The effectiveness of LPS is evaluated on time series classification problems from various domains. We compare LPS to eleven well-known similarity measures. Our experimental results show that LPS provides fast and competitive results on benchmark datasets from several domains. Furthermore, LPS provides a research direction and template approach that breaks from the linear dependency models to potentially foster other promising nonlinear approaches. A family of probabilistic time series models is developed to analyze the time evolution of topics in large document collections. The approach is to use state space models on the natural parameters of the multinomial distributions that represent the topics. Variational approximations based on Kalman filters and nonparametric wavelet regression are developed to carry out approximate posterior inference over the latent topics. In addition to giving quantitative, predictive models of a sequential corpus, dynamic topic models provide a qualitative window into the contents of a large document collection. The models are demonstrated by analyzing the OCR'ed archives of the journal Science from 1880 through 2000. From the Publisher: This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.