Threshold based partial partitioning fuzzy means clustering algorithm (TPPFMCA) for pattern discovery

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Fuzzy C-means is very popular data clustering algorithm use in many systems modeling to determine system behavior in concise way. However, it requires the specifications of numbers of clusters in advance, which is not feasible in many system modeling. Prediction Models, based on web caching and prefetching, are such modeling systems in which to predict numbers of clusters in advance is quite impossible so Fuzzy C-means algorithm is in original way is not suit to such modeling. In this paper, new clustering algorithm is proposed which is fusion of Fuzzy Means and threshold concepts. The paper exhibits experiments of the proposed algorithm in context to web caching and prefetching model. The paper also compares the result of this algorithm with familiar Markov Model.

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Correspondence to Dharmendra Patel.



  1. 1.

    Pattern discovery steps and coding based on Markov Model

    Markovian Test-1

    • Test description To generate occurrence matrix that determines occurrences of particular web object from current state.

    • Result Occurrence matrix is generated (refer Table 5.3)

    • Tools used Microsoft Excel Tool is used for this experiment. One macro is generating to determine number of occurrences.

    • Macro code Following code is generated for that.


    Markovian Test-2

    Test description To generate transition probability matrix based on current state.

    In order to generate transition probability matrix number of tests is carried out.

    1. (a)

      Test 1 Determine summation of number of occurrences from current state to all other states.

      Tools used Microsoft Excel

      Query SUM(X: Y) Where X and Y are cell numbers.

      Result It generates summation figure from current state to all other states.

    2. (b)

      Test 2 Generate transition probability from current state to all other states.

      • Tools used Microsoft Excel

      • Query SUM(X: Y)/N Where N is addition that is generated from test-1.

      • Result It generates transition probability value of every cell from one cell to another.

    3. (c)

      Test 3 To determine maximum value of transition probability in order to predict next web object.

      • Tools used Microsoft Excel.

      • Query MAX(X: Y).

      • Result Prediction of Next Web Object.

  2. 2.

    Pattern discovery steps and coding based on distance measurement techniques


    • Test description To determine distance measure between web sessions according to Lavensthein distance measurement technique.

    • Tool used One online tool is used to determine distance measure between web sessions. Reference is

    • Results One metric with distance value is generated as a result of this test.


    • Test description To determine proximity of different web sessions according to Lavensthein measurement technique.

    • Tool used Microsoft Excel tool is used to determine proximity based on conditional formatting option. Metric generated in previous test result is used as an input.

    • Results As results of this test number of sessions involved in each cluster is determined based on particular threshold value.


    • Test description To determine accuracy of pattern.

    • Tool used Microsoft Excel tool is used to determine accuracy of pattern. Accuracy of pattern is determine by taking average of each permutation combination web session pair.

    • Results Accuracy value is generating for each pattern.


    • Test description To determine mean and standard deviation in order to take appropriate action.

    • Tool used Microsoft Excel tool is used to determine mean and standard deviation of patterns generated at specific threshold value.

    • Results Mean and standard deviation of patterns are generated as a result of test.

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Cite this article

Patel, D. Threshold based partial partitioning fuzzy means clustering algorithm (TPPFMCA) for pattern discovery. Int. j. inf. tecnol. (2019) doi:10.1007/s41870-019-00343-5

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  • Fuzzy C-means
  • Clustering
  • Web caching
  • Web prefetching
  • Markov model