In many emerging applications, data streams are monitored in a network environment. Due to limited communication bandwidth and other resource constraints, a critical and practical demand is to online compress data streams continuously with quality guarantee. Although many data compression and digital signal processing methods have been developed to reduce data volume, their super-linear time and more-than-constant space complexity prevents them from being applied directly on data streams, particularly over resource-constrained sensor networks. In this paper, we tackle the problem of online quality guaranteed compression of data streams using fast linear approximation (i.e., using line segments to approximate a time series). Technically, we address two versions of the problem which explore quality guarantees in different forms. We develop online algorithms with linear time complexity and constant cost in space. Our algorithms are optimal in the sense they generate the minimum number of segments that approximate a time series with the required quality guarantee. To meet the resource constraints in sensor networks, we also develop a fast algorithm which creates connecting segments with very simple computation. The low cost nature of our methods leads to a unique edge on the applications of massive and fast streaming environment, low bandwidth networks, and heavily constrained nodes in computational power. We implement and evaluate our methods in the application of an acoustic wireless sensor network.
@cite_7 , the authors use PLA to estimate a time series. But the authors put unnecessary constraints on the algorithm, which requires the endpoints come from the original dataset. On the whole, their algorithm can run in @math time complexity and takes @math space complexity.
@cite_7
1552695456 2114001875 2097983034 2520179645
Similarity-based search over time-series databases has been a hot research topic for a long history, which is widely used in many applications, including multimedia retrieval, data mining, web search and retrieval, and so on. However, due to high dimensionality (i.e. length) of the time series, the similarity search over directly indexed time series usually encounters a serious problem, known as the "dimensionality curse". Thus, many dimensionality reduction techniques are proposed to break such curse by reducing the dimensionality of time series. Among all the proposed methods, only Piecewise Linear Approximation (PLA) does not have indexing mechanisms to support similarity queries, which prevents it from efficiently searching over very large time-series databases. Our initial studies on the effectiveness of different reduction methods, however, show that PLA performs no worse than others. Motivated by this, in this paper, we re-investigate PLA for approximating and indexing time series. Specifically, we propose a novel distance function in the reduced PLA-space, and prove that this function indeed results in a lower bound of the Euclidean distance between the original time series, which can lead to no false dismissals during the similarity search. As a second step, we develop an effective approach to index these lower bounds to improve the search efficiency. Our extensive experiments over a wide spectrum of real and synthetic data sets have demonstrated the efficiency and effectiveness of PLA together with the newly proposed lower bound distance, in terms of both pruning power and wall clock time, compared with two state-of-the-art reduction methods, Adaptive Piecewise Constant Approximation (APCA) and Chebyshev Polynomials (CP). 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. The problem of efficiently and accurately locating patterns of interest in massive time series data sets is an important and non-trivial problem in a wide variety of applications, including diagnosis and monitoring of complex systems, biomedical data analysis, and exploratory data analysis in scientific and business time series. In this paper a probabilistic approach is taken to this problem. Using piecewise linear segmentations as the underlying representation, local features (such as peaks, troughs, and plateaus) are defined using a prior distribution on expected deformations from a basic template. Global shape information is represented using another prior on the relative locations of the individual features. An appropriately defined probabilistic model integrates the local and global information and directly leads to an overall distance measure between sequence patterns based on prior knowledge. A search algorithm using this distance measure is shown to efficiently and accurately find matches for a variety of patterns on a number of data sets, including engineering sensor data from space Shuttle mission archives. The proposed approach provides a natural framework to support user-customizable "query by content" on time series data, taking prior domain information into account in a principled manner. Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences continuously measured by weather stations across the US. These data are often referred to as un structured. The first task in its analytics is to derive a low dimensional representation, a graph or discrete manifold, that describes well the inter relations among the time series and their intra relations across time. This paper presents a computationally tractable algorithm for estimating this graph that structures the data. The resulting graph is directed and weighted, possibly capturing causal relations, not just reciprocal correlations as in many existing approaches in the literature. A convergence analysis is carried out. The algorithm is demonstrated on random graph datasets and real network time series datasets, and its performance is compared to that of related methods. The adjacency matrices estimated with the new method are close to the true graph in the simulated data and consistent with prior physical knowledge in the real dataset tested.