A New Method for Piecewise Linear Representation of Time Series Data

Zhou, Jiajie; Yu, Gang; Yu, Daren

doi:10.1016/j.phpro.2012.03.205

Cited by 12 publications

(3 citation statements)

References 3 publications

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“…Prior works show that many types of signals [33,34], e.g. EEG and ECG signals, often reveals approximately piecewise smooth structure [35][36][37][38]. This structure exhibits gradient sparsity, i.e.…”

Section: Multiple-integer-order-difference Matrixmentioning

confidence: 99%

Training-free compressed sensing for wireless neural recording using analysis model and group weighted ${{\ell}_{1}}$ -minimization

2017

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Section: Multiple-integer-order-difference Matrixmentioning

confidence: 99%

Training-free compressed sensing for wireless neural recording using analysis model and group weighted ${{\ell}_{1}}$ -minimization

2017

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“…The first part predicts the standard deviations σ fi using maximum likelihood estimation. Once the variances are estimated, simple quadratic regression can be employed to solve for a i , b i , and c i in the following equation, derived from (27),…”

Section: Weighted Analysis ℓ 1 -Minimizationmentioning

confidence: 99%

Compressed Sensing for Implantable Neural Recordings Using Co-sparse Analysis Model and Weighted $\ell_1$-Optimization

Sun¹,

Zhao²,

Zhu³

2016

Preprint

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Reliable and energy-efficient wireless data transmission remains a major challenge in resourceconstrained wireless neural recording tasks, where data compression is generally adopted to relax the burdens on the wireless data link. Recently, Compressed Sensing (CS) theory has successfully demonstrated its potential in neural recording application. The main limitation of CS, however, is that the neural signals have no good sparse representation with commonly used dictionaries and learning a reliable dictionary is often data dependent and computationally demanding. In this paper, a novel CS approach for implantable neural recording is proposed. The main contributions are: 1) The co-sparse analysis model is adopted to enforce co-sparsity of the neural signals, therefore overcoming the drawbacks of conventional synthesis model and enhancing the reconstruction performance. 2) A multi-fractional-order difference matrix is constructed as the analysis dictionary, thus avoiding the dictionary learning procedure and reducing the need for previously acquired data and computational resources. 3) By exploiting the statistical priors of the analysis coefficients, a weighted analysis ℓ 1 -minimization (WALM) algorithm is proposed to reconstruct the neural signals. Experimental results on Leicester neural signal database reveal that the proposed approach outperforms the state-of-the-art CS-based methods. On the challenging high compression ratio task, the proposed approach still achieves high reconstruction performance and spike classification accuracy.

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“…Zhou et al suggest using points at which slope changes significantly as breakpoints [9]. Yuelong et al segment a time series at points at which the signal value differs from its immediate neighbor by more than a pre-specified threshold [10].…”

Section: B Non-uniform Segmentationmentioning

confidence: 99%

Two Stage Segmentation for Efficient Time Series Matching

2014

2nd International Conference on Research in Science, Engineering and Technology (ICRSET’2014), March 21-22, 2014 Dubai (UAE)

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The piecewise linear approximation (PLA) reduces the dimensionality of time series data by first partitioning the time series into segments and representing each segment by a straight line. The reconstruction accuracy of piecewise linear approximation depends on the number of segments used, and the location of breakpoints. This paper presents a segmentation approach that identifies breakpoints in two stages. First, the time series is partitioned into subsequences by identifying perceptually important local maxima and minima as breakpoints. In the second stage, each subsequence is recursively partitioned into two segments at the optimal breakpoint to the desired degree of accuracy. The proposed segmentation method leads to a PLA representation which, in addition to high reconstruction accuracy, has the ability to support piecewise time series matching not adequately supported by most representations. The construction of sub-optimal PLA representation takes linear time, and can be extended to build sub-optimal piecewise polynomial representations.

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A New Method for Piecewise Linear Representation of Time Series Data

Cited by 12 publications

References 3 publications

Training-free compressed sensing for wireless neural recording using analysis model and group weighted ${{\ell}_{1}}$ -minimization

Training-free compressed sensing for wireless neural recording using analysis model and group weighted ${{\ell}_{1}}$ -minimization

Compressed Sensing for Implantable Neural Recordings Using Co-sparse Analysis Model and Weighted $\ell_1$-Optimization

Two Stage Segmentation for Efficient Time Series Matching

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