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piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2018年第16期88卷 3193-3216页

作者： Arbenz, Philipp Guevara-Alarcon, William SCOR Switzerland Ltd Zurich Switzerland Swiss Fed Inst Technol Zurich Switzerland Univ Lausanne Extranef Of 105 CH-1015 Lausanne Switzerland

Big data applications and Monte Carlo simulation results can nowadays easily contain data sets in the size of millions of entries. We consider the situation when the information on a large univariate data set or sample needs to be preserved, stored or transferred. We suggest an algorithm to approximate a univariate empirical distribution through a piecewise linear distribution which requires significantly less memory to store. The approximation is chosen in a computationally efficient manner, such that it preserves the mean, and its Wasserstein distance to the empirical distribution is sufficiently small.

关键词： Monte Carlo simulation empirical distribution piecewise linear approximation Wasserstein distance compression

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Streaming piecewise linear approximation for Efficient Data Management in Edge Computing 19

Streaming Piecewise Linear Approximation for Efficient Data ...

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34th ACM/SIGAPP Annual International Symposium on Applied Computing (SAC)

作者： Duvignau, Romaric Gulisano, Vincenzo Papatriantafilou, Marina Savic, Vladimir Chalmers Univ Technol CTH Gothenburg Sweden

ISBN: (纸本)9781450359337

In our digitalization era, where large and continuous data streams are produced by an ever increasing number of sensors, data retrieval and storage from edge devices is hampered when data volumes exceed the communication bandwidth of cyber-physical systems. piecewise linear approximation (PLA), which trades space against precision by representing some portion of data by segments, could reduce the volume of transmitted and stored data and thus be beneficial to a wide range of edge/ fog system architectures, saving communication bandwidth and addressing the aforementioned drawback. Porting a well-established tool such as PLA into the streaming paradigm is nonetheless challenging, and attention has to be payed to balance achievable compression, delays and imprecision. We analyze such challenges and propose different solutions to meet them. Our main contribution is a set of streaming PLA techniques that allow compression of the input data stream on the fly, tolerating a bounded maximum error. Through an experimental study based on real data, we demonstrate the superiority of our techniques in all sought aspects over preceding methods.

关键词： data compression piecewise linear approximation edge computing

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Data piecewise linear approximation for Bearings Degradation Monitoring 10

Data Piecewise Linear Approximation for Bearings Degradation...

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10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems - Technology and Applications (IDAACS)

作者： Huang, Fei Sava, Alexandre Adjallah, Kondo H. Wang, Zhouhang Univ Lorraine Lab Concept Optimisat & Modelisat Syst LCOMS EA 7306 F-57000 Metz France Huaiyin Inst Technol 1 Meicheng Rd Huaian 223003 Jiangsu Peoples R China

ISBN: (纸本)9781728140698

In this paper, we propose a method based on piecewise linear approximation (PLA) with segmented projection error (SPE) to reveal the underlying correlation structures and approximate multivariate time series. Based on this method we elaborate an indicator called vector of segmented projection error (VSPE) to characterize the bearings degradation using standard time domain standard features extracted from the vibration signal. The indicator VSPE monitors the evolution of the entire degradation process efficiently and provides real-time information on bearings degradation. We show the effectiveness of this new indicator using benchmark data. The results reveal the sensitive and monotonic character of the indicator VSPE according to the bearings degradation, which is promising for monitoring bearings on their lifespan.

关键词： piecewise linear approximation segmented projection error VSPE

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Fast Multi-output Regression Based on piecewise linear approximation

Fast Multi-output Regression Based on Piecewise Linear Appro...

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International Conference on Information Science and Control Engineering (ICISCE)

作者： Zhihui Li Shuai Wang Yongmei Liu Yufei Huang Jing Zhang School of Computer Science and Technology Harbin Engineering University Harbin China Beijing Institute of Spacecraft System Engineering Beijing China School of Information Science and Engineering University of Jinan Jinan China

In this paper a fast Multi-output Regression algorithm is implemented based on piecewise linear approximation (PLA). Maximum distance point splitting is used to fit lines piecewisely. Then the best knot set of linear segmentation is obtained. The independent variable X is divided into some linear intervals, which make it possible that linear regression is implemented in fast and accurate way. The knot set with the smallest error in all dimensions of dependent variable is used as the node partition scheme. The matrix of regression model is derived by the least square. The Experiment results prove that the algorithm achieves the performance of the state-of-the-art with predicting time below millisecond.

关键词： piecewise linear approximation linear regression Programmable logic arrays Predictive models approximation algorithms Prediction algorithms Classification algorithms

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piecewise linear approximation of Vector-Valued Images and Curves via Second-Order Variational Model

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2017年第9期26卷 4414-4429页

作者： Zanetti, Massimo Bruzzone, Lorenzo Univ Trento Dept Informat Engn & Comp Sci I-38123 Trento Italy

Variational models are known to work well for addressing image restoration/regularization problems. However, most of the methods proposed in the literature are defined for scalar inputs and are used on multiband images (such as RGB or multispectral imagery) by the composition of a simple band-wise processing. This involves suboptimal results and may introduce artifacts. Only in a few cases, variational models are extended to the case of vector-valued inputs. However, the known implementations are restricted to the first-order models, while the secondorder models are never considered. Thus, typical problems of the first-order models, such as the staircasing effect cannot be overtaken. This paper considers a second-order functional model to function approximation with free discontinuities given by Blake-Zisserman (BZ) and proposes an efficient minimization algorithm in the case of vector-valued inputs. In the BZ model, the Hessian of the solution is penalized outside a set of finite length, therefore the solution is forced to be piecewise linear. Moreover, the model allows the formation of free discontinuities and free gradient discontinuities. The proposed algorithm is applied to difficult color image restoration/regularization problems and to piecewise linear approximation of curves in space.

关键词： Multiband image variational methods Blake-Zisserman Mumford-Shah piecewise linear approximation block-coordinate descent method

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A Generic Storage Model Based on a Future Cost piecewise-linear approximation

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IEEE TRANSACTIONS ON SMART GRID 2019年第1期10卷 878-888页

作者： Alvarez, Manuel Ronnberg, Sarah K. Bermudez, Juan Zhong, Jin Bollen, Math H. J. Lulea Univ Technol Dept Engn Sci & Math S-93187 Skelleftea Sweden Univ Simon Bolivar Dept Energy Convers & Transport Caracas 01080 Venezuela Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China

This paper presents a generic storage model (GSM) inspired by the scheduling of hydraulic reservoirs. The model for steady state short-term operational studies interlaces with the long-term (LT) energy scheduling through a piecewise-linear future cost function (FCF). Under the assumption that a stochastic dual dynamic programming approach has been used to solve the energy schedule for the LT, the FCF output from that study will be processed to obtain an equivalent marginal opportunity cost for the storage unit. The linear characteristic of a segment of the FCF will allow a linear modeling of the storage unit production cost. This formulation will help to coordinate the renewable resource along with storage facilities in order to find the optimal operation cost while meeting end-point conditions for the LT plan of the energy storage. The generic model will be implemented to represent a battery storage and a pumped-hydro storage. A stochastic unit commitment with the GSM will be formulated and tested to assess the day-ahead scheduling strategy of a virtual power plant facing uncertainties from production, consumption, and market prices.

关键词： Energy storage piecewise linear approximation optimal scheduling uncertainty

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Time and Memory Efficient Online piecewise linear approximation of Sensor Signals

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SENSORS 2018年第6期18卷 1672-1672页

作者： Gruetzmacher, Florian Beichler, Benjamin Hein, Albert Kirste, Thomas Haubelt, Christian Univ Rostock Inst Appl Microelect & Comp Engn D-18051 Rostock Germany Univ Rostock Inst Comp Sci D-18051 Rostock Germany

piecewise linear approximation of sensor signals is a well-known technique in the fields of Data Mining and Activity Recognition. In this context, several algorithms have been developed, some of them with the purpose to be performed on resource constrained microcontroller architectures of wireless sensor nodes. While microcontrollers are usually constrained in computational power and memory resources, all state-of-the-art piecewise linear approximation techniques either need to buffer sensor data or have an execution time depending on the segment's length. In the paper at hand, we propose a novel piecewise linear approximation algorithm, with a constant computational complexity as well as a constant memory complexity. Our proposed algorithm's worst-case execution time is one to three orders of magnitude smaller and its average execution time is three to seventy times smaller compared to the state-of-the-art piecewise linear approximation (PLA) algorithms in our experiments. In our evaluations, we show that our algorithm is time and memory efficient without sacrificing the approximation quality compared to other state-of-the-art piecewise linear approximation techniques, while providing a maximum error guarantee per segment, a small parameter space of only one parameter, and a maximum latency of one sample period plus its worst-case execution time.

关键词： piecewise linear approximation segmentation sensor data abstraction sensor signal compression CPLR wireless sensor networks embedded sensor processing

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L₁ Discretization for Sampled-Data Controller Synthesis via piecewise linear approximation

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2016年第5期61卷 1143-1157页

作者： Kim, Jung Hoon Hagiwara, Tomomichi Kyoto Univ Dept Elect Engn Kyoto 6158510 Japan Korea Inst Sci & Technol Ctr Robot Res Seoul 136791 South Korea

This paper develops a new discretization method with piecewise linear approximation for the L-1 optimal controller synthesis problem of sampled-data systems, which is the problem of minimizing the L infinity-induced norm of sampled-data systems. We apply fast-lifting on the top of the lifting technique, by which the sampling interval [0, h) is divided into M subintervals with an equal width. The signals on each subinterval are then approximated by linear functions by introducing two types of 'linearizing operators' for input and output, which leads to piecewise linear approximation of sampled-data systems. By using the arguments of preadjoint operators, we provide an important inequality that forms a theoretical basis for tackling the L-1 optimal controller synthesis problem of sampled-data systems more efficiently than the conventional method. More precisely, a mathematical basis for the piecewise linear approximation method associated with the convergence rate is shown through this inequality, and this suggests that the piecewise linear approximation method may drastically outperform the conventional method in the L-1 optimal controller synthesis problem of sampled-data systems. We then provide a discretization procedure of sampled-data systems by which the L-1 optimal controller synthesis problem is converted to the discrete-time l(1) optimal controller synthesis problem. Finally, effectiveness of the proposed method is demonstrated through a numerical example.

关键词： Fast-lifting L-1 optimal control piecewise linear approximation sampled-data systems

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EXPERT SYSTEMS WITH APPLICATIONS 2015年第21期42卷 7664-7675页

作者： Banko, Zoltan Abonyi, Janos Univ Pannonia Dept Proc Engn H-8200 Veszprem Hungary

In recent years, expert systems built around time series-based methods have been enthusiastically adopted in engineering applications, thanks to their ease of use and effectiveness. This effectiveness depends on how precisely the raw data can be approximated and how precisely these approximations can be compared. When performance of a time series-based system needs to be improved, it is desirable to consider other time series representations and comparison methods. The approximation, however, is often generated by a non-replaceable element and eventually the only way to find a more advanced comparison method is either by creating a new dissimilarity measure or by improving the existing one further. In this paper, it is shown how a mixture of different comparison methods can be utilized to improve the effectiveness of a system without modifying the time series representation itself. For this purpose, a novel, mixed comparison method is presented for the widely used piecewise linear approximation (PLA), called mixed dissimilarity measure for PLA (MDPLA). It combines one of the most popular dissimilarity measure that utilizes the means of PLA segments and the authors' previously presented approach that replaces the mean of a segment with its slope. On the basis of empirical studies three advantages of such combined dissimilarity measures are presented. First, it is shown that the mixture ensures that MDPLA outperforms the most popular dissimilarity measures created for PLA segments. Moreover, in many cases, MDPLA provides results that makes the application of dynamic time warping (DTW) unnecessary, yielding improvement not only in accuracy but also in speed. Finally, it is demonstrated that a mixed measure, such as MDPLA, shortens the warping path of DTW and thus helps to avoid pathological warpings, i.e. the unwanted alignments of DTW. This way, DTW can be applied without penalizing or constraining the warping path itself while the chance of the unwanted alignments ar

关键词： Dynamic time warping Local distance piecewise linear approximation Similarity Constraining

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A New Method of piecewise linear approximation of Non-stationary Time Series for Similarity Measurement 12

A New Method of Piecewise Linear Approximation of Non-statio...

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12th International Conference on Electronics Computer and Computation (ICECCO)

作者： Satybaldiev, Daniiar Int Ataturk Alatoo Univ Dept Elect & Nano Elect Engn Fac New Technol Bishkek Kyrgyzstan

ISBN: (纸本)9781509001996

As much of data and information are performed over time they are represented in a form of time series. The amount of information increases with tremendous speed that should be stored and analyzed. Extracting meaningful information from the stock of data is called time series data mining. Important part of time series data mining is similarity search of time series. The new method is developed for time series representation in a form of piecewise linear form which was taken as a base for building as criteria for similarity search of time series. The main approach based on our work will be discussed in this article.

关键词： piecewise Polynomial Aggregate support points multiple nonlinear regressions piecewise linear approximation

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