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A bidirectional weighted boundary distance algorithm for time series similarity computation based on optimized sliding window size

  • * Corresponding author: Zhaohui Tang

    * Corresponding author: Zhaohui Tang 
Abstract Full Text(HTML) Figure(12) / Table(4) Related Papers Cited by
  • The existing method of determining the size of the time series sliding window by empirical value exists some problems which should be solved urgently, such as when considering a large amount of information and high density of the original measurement data collected from industry equipment, the important information of the data cannot be maximally retained, and the calculation complexity is high. Therefore, by studying the effect of sliding window on time series similarity technology in practical application, an algorithm to determine the initial size of the sliding window is proposed. The upper and lower boundary curves with a higher fitting degree are constructed, and the trend weighting is introduced into the $ LB\_Hust $ distance calculation method to reduce the difficulty of mathematical modeling and improve the efficiency of data similarity computation.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

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  • Figure 1.  Distance between three series

    Figure 2.  The sliding window principle

    Figure 3.  The normalized state of 6 types time serie

    Figure 4.  Quadratic distribution of window size

    Figure 5.  Steplength range

    Figure 6.  Time series of the three generators

    Figure 7.  Clustering result comparison

    Figure 8.  Clustering error rate with different weight coefficients

    Figure 9.  Precision of five methods on5 data sets

    Figure 10.  Clustering error rate with different weight coefficients

    Figure 11.  Precision of five methods on5 data sets

    Figure 12.  Runtime of five methods on 5 data sets

    Table 1.  Dataset attribute

    Type Items Status
    1 1-100 Normal
    2 101-200 Cyclic
    3 201-300 Increasing trend
    4 301-400 Decreasing trend
    5 401-500 Upward shift
    6 501-600 Downward shift
     | Show Table
    DownLoad: CSV

    Table 2.  the combination value of $ {w_s} $ and $ {L_s} $ and the corresponding distance $ {D_T} $

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
    2 49.1 - - - - - - - - - - - - - -
    3 55.4 - - - - - - - - - - - - - -
    4 54.8 60.6 - - - - - - - - - - - - -
    5 58.7 61.2 - - - - - - - - - - - - -
    6 64.3 65.3 60.0 - - - - - - - - - - - -
    7 62.5 63.9 61.3 - - - - - - - - - - - -
    8 64.8 65.6 64.0 62.6 - - - - - - - - - - -
    9 62.5 61.2 63.5 62.3 - - - - - - - - - - -
    10 63.4 63.9 59.1 62.9 60.8 - - - - - - - - - -
    11 58.0 61.9 62.1 58.5 60.1 - - - - - - - - - -
    12 61.3 61.2 58.3 61.1 60.9 59.1 - - - - - - - - -
    13 60.2 59.9 59.1 49.3 58.2 49.3 - - - - - - - - -
    14 49.9 59.6 60.2 60.8 59.1 60.1 61.7 - - - - - - - -
    15 55.9 56.2 53.2 48.2 60.2 49.2 58.7 - - - - - - - -
    16 60.9 55.2 58.3 58.0 52.1 50.0 56.1 49.0 - - - - - - -
    17 49.2 53.1 54.4 55.2 60.8 59.4 51.7 53.3 - - - - - - -
    18 53.7 54.4 52.0 52.3 52.8 60.1 59.2 49.2 49.2 - - - - - -
    19 58.3 60.8 55.1 50.3 58.7 58.0 58.1 53.0 51.9 - - - - - -
    20 50.7 53.3 55.8 50.1 42.3 45.7 50.0 51.2 51.2 46.3 - - - - -
    21 49.6 50.2 46.9 46.5 47.2 47.1 47.5 46.0 48.2 43.9 - - - - -
    22 51.3 49.9 48.2 46.7 50.0 45.0 40.0 39.2 39.5 40.7 39.1 - - - -
    23 39.9 54.2 50.0 49.8 49.0 36.8 36.5 38.1 42.5 43.9 35.9 - - - -
    24 46.8 51.9 48.3 45.0 38.2 42.7 39.4 50.2 41.9 38.4 43.3 51.8 - - -
    25 51.6 40.0 58.7 43.1 40.0 39.4 35.0 45.3 45.9 41.2 38.1 40.9 - - -
    26 47.3 48.6 50.3 39.6 42.6 55.2 42.0 36.1 35.0 42.0 43.8 39.5 47.8 - -
    27 47.5 51.3 40.0 41.6 39.5 35.0 50.0 49.2 39.4 38.4 35.6 39.2 49.9 - -
    28 45.0 40.4 38.4 35.0 35.7 46.2 50.6 45.2 39.1 39.6 42.1 48.2 40.0 38.9 -
    29 50.1 48.3 40.2 41.6 35.9 36.1 40.3 39.4 50.1 46.3 39.6 35.9 35.9 35.0 -
    30 42.2 49.8 45.0 39.2 40.0 38.9 40.4 39.3 37.5 38.6 36.3 36.9 35.0 36.2 35.2
     | Show Table
    DownLoad: CSV

    Table 3.  5 Groups Dataset

    Dataset Samples Categories Attributes
    temperature 148 3 2
    pressure 169 4 12
    position 327 10 17
    concentration 112 6 16
    flow rate 236 5 7
     | Show Table
    DownLoad: CSV

    Table 4.  Cross-validation results

    Dataset The optimal value Average precision
    $ {w_s} $ $ {w_n} $ $ {w_p} $ test set training set
    temperature 8 0.6 0.4 $ {\rm{90\% }} $ $ {\rm{92\% }} $
    pressure 9 0.6 0.4 $ {\rm{89\% }} $ $ {\rm{91\% }} $
    position 8 0.6 0.4 $ {\rm{91\% }} $ $ {\rm{92\% }} $
    concentration 8 0.6 0.4 $ {\rm{90\% }} $ $ {\rm{91\% }} $
    flow rate 8 0.6 0.4 $ {\rm{90\% }} $ $ {\rm{92\% }} $
     | Show Table
    DownLoad: CSV
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