A novel multi-resolution representation for time series sensor data analysis

  • Yupeng Hu
  • Cun Ji
  • Qingke Zhang
  • Lin Chen
  • Peng Zhan
  • Xueqing LiEmail author
Methodologies and Application


The evolution of IoT has increased the popularity of all types of sensing devices in a variety of industrial fields and has resulted in enormous growth in the volume of sensor data. Considering the high volume and dimensionality of sensor data, the ability to perform in-depth data analysis and data mining tasks directly on the raw time series sensor data is limited. To solve this problem, we propose a novel dimensional reduction and multi-resolution representation approach for time series sensor data. This approach utilizes an appropriate number of important data points (IDPs) within a certain time series sensor data to produce a corresponding multi-resolution piecewise linear representation (MPLR), called MPLR-IDP. The results of the theoretical analyses and experiments show that MPLR-IDP can reduce the dimensionality while maintaining the important characteristics of time series data. MPLR-IDP can represent the data in a more flexible way to meet diverse needs of different users.


Internet of things Time series Piecewise linear representation Multi-resolution representation 



A time series with length n


Piecewise linear representation


Multi-resolution PLR


The basic multi-resolution PLR


The extended multi-resolution PLR


Perceptually important points


Turning points


Important data points


Time series representation standards


The user-specified number of segments


The user-specified fitting error of entire time series


The user-specified maximum fitting error of segment


Adaptive representation index


Specialized binary tree index


The optimal binary search tree


Linear interpolation


Linear regression

\(seg{{<}} {x},{y}{>}\)

Segment object from \(v_x\) to \(v_{y}\)

\(es_{{<} x,y{>}}\)

The fitting error of \(seg{<} {x},{y}{>}\)


Basic multi-resolution PLR


Extended multi-resolution PLR


The time series dataset with m time series


The maximum number of TPs


Data compression ratio


Time series classification


Shapelet transformation


Time series training dataset


All the time series subsequences set


The final shapelets set



The authors would like to thank the anonymous reviewers and the editors for their insightful comments and suggestions, which are greatly helpful for improving the quality of this paper. This work is supported by the National Natural Science Foundation of China, No.: 61772310, No.: 61702300, No.: 61702302, No.: 61802231; the Science and Technology Development Funds of Shandong Province, No.: 2014GGX101028; the Project of Qingdao Postdoctoral Applied Research.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyShandong UniversityTsingtaoChina
  2. 2.School of Information Science and EngineeringShandong Normal UniversityJinanChina
  3. 3.School of SoftwareShandong UniversityJinanChina

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