An Improved Piecewise Aggregate Approximation Based on Statistical Features for Time Series Mining

Guo, Chonghui; Li, Hailin; Pan, Donghua

doi:10.1007/978-3-642-15280-1_23

Cited by 43 publications

(21 citation statements)

References 11 publications

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“…The distance functions [19] for the representations of PAA and SAX are lower-bound on Euclidean distance. An improved PAA [35] considering standard variance of each segment was proposed, and the corresponding function was also lower-bound on Euclidean distance. And more importantly, some efficient distance functions [3,13,24,[26][27][28] were lower-bound on DTW.…”

Section: Dynamic Time Warpingmentioning

confidence: 99%

Piecewise aggregate representations and lower-bound distance functions for multivariate time series

2015

Physica A: Statistical Mechanics and its Applications

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Section: Dynamic Time Warpingmentioning

confidence: 99%

Piecewise aggregate representations and lower-bound distance functions for multivariate time series

2015

Physica A: Statistical Mechanics and its Applications

Self Cite

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“…Then, these mean values can be indexed efficiently in a lower dimensionality space. This method may miss some important information and sometimes cause inaccurate results in time series mining, so Guo et al [17] presented an improved PAA based on statistical features including a mean-based feature and variance-based feature. Besides, Fotso et al [18] presented a heuristic for time series compression with PAA.…”

Section: Related Workmentioning

confidence: 99%

Fast Piecewise Polynomial Fitting of Time-Series Data for Streaming Computing

Gao

Zhang

et al. 2020

IEEE Access

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Streaming computing attracts intense attention because of the demand for massive data analyzing in real-time. Due to unbounded and continuous input, the volume of streaming data is so high that all the data cannot be permanently stored. Piecewise polynomial fitting is a popular data compression method that approximately represents the raw data stream with multiple polynomials. The polynomial coefficients corresponding to the best-fitting curve can be calculated by the method of least squares, which minimizes the sum of the squared residuals between observed and fitted values. However, built on several matrix calculations, the method of least squares always leads to high time complexity and is difficult to be applied to streaming computing. This paper puts forward a fast piecewise polynomial fitting for time-series data in streaming computing. The input data stream is dynamically segmented according to a given residual bound. Meanwhile, the data points in each segment are fitted using an improved polynomial fitting method, which has less time overhead than general polynomial fitting by reusing the intermediate calculation results. Experimental results on four time-series datasets show that our algorithm can achieve the highest speedup to the general piecewise polynomial fitting of 2.82x for periodically sampled time-series data and 1.85x for aperiodically sampled time-series data, without affecting the compression ratio and fitting accuracy. Moreover, the event-time latency comparison in a streaming environment indicates that the improved method can endure higher throughput than general piecewise polynomial fitting with the same latency. INDEX TERMS Least squares, piecewise polynomial fitting, streaming computing, time-series data.

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“…There has been much work in dimensional reduction, and one of the popular approaches is using spatial method to index the data in the transformed space including Discrete Fourier Transform (DFT) [7,14], Singular Value Decomposition (SVD) [7,12], Discrete Wavelet Transform (DWT) [3,11]. And there are piecewise aggregate representation including Piecewise Aggregate Approximation (PAA) [8,12], Symbolic Aggregate approximation (SAX) [14,21]. PAA is competitive with or faster than other methods and it is easy to implement, which allows more flexible distance measure.…”

Section: Introductionmentioning

confidence: 99%

An Improvement of PAA on Trend-Based Approximation for Time Series

Zhang

Chen

Yin

et al. 2018

Lecture Notes in Computer Science

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Piecewise Aggregate Approximation (PAA) is a competitive basic dimension reduction method for high-dimensional time series mining. When deployed, however, the limitations are obvious that some important information will be missed, especially the trend. In this paper, we propose two new approaches for time series that utilize approximate trend feature information. Our first method is based on relative mean value of each segment to record the trend, which divide each segment into two parts and use the numerical average respectively to represent the trend. We proved that this method satisfies lower bound which guarantee no false dismissals. Our second method uses a binary string to record the trend which is also relative to mean in each segment. Our methods are applied on similarity measurement in classification and anomaly detection, the experimental results show the improvement of accuracy and effectiveness by extracting the trend feature suitably.

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An Improved Piecewise Aggregate Approximation Based on Statistical Features for Time Series Mining

Cited by 43 publications

References 11 publications

Piecewise aggregate representations and lower-bound distance functions for multivariate time series

Piecewise aggregate representations and lower-bound distance functions for multivariate time series

Fast Piecewise Polynomial Fitting of Time-Series Data for Streaming Computing

An Improvement of PAA on Trend-Based Approximation for Time Series

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