Single Pass Clustering

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Single Pass Clustering

• Jieh-Shan George Yeh

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Example

• Consider the set of documents and terms
• Clustering the terms using the single pass method
  (using the term vector columns)

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Preliminary

• Order the term vectors (column vectors).
• Choose a simplicity function, say, dot product.
• Set a pre-specified similarity threshold 10.

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Step 1

• Start with T1 in a cluster by itself, say C1.
• At this point, C1 contains only one item, T1.
• the centroid of C1 is simply the vector for T1
  C1 lt1, 3, 3, 2, 2gt.

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Step 2

• Now compare (i.e., measure similarities) of the
  next item (T2) to centroids of all existing
  clusters.
• SIM(T2, C1) lt2, 1, 0, 1, 2gtlt1, 3, 3, 2, 2gt 21
  13 03 12 22 11 gt10
• Add T2 to cluster C1.
• Compute the new centroid for C1 (which now
  contains T1 and T2).
• The centroid (which is the average vector for T1
  and T2 is
• C1 lt3/2, 4/2, 3/2, 3/2, 4/2gt

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Step 3

• Now, there is only one cluster, C1, so we only
  need to compare T3 with C1 centroid.
• SIM(T3, C1) 0 8/2 0 0 4/2 6 lt10
• Therefore, we use T3 to start a new cluster, C2.
• Now we have two clusters
• C1 T1, T2
• C2 T3

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Step 4

• Move to the next unclustered item, T4.
• SIM(T4, C1) lt0, 3, 0, 3, 5gtlt3/2, 4/2, 3/2, 3/2,
  4/2gt 0 12/2 0 9/2 20/2 20.5 gt10
• SIM(T4, C2) lt0, 3, 0, 3, 5gt lt0, 2, 0, 0, 1gt 0
  6 0 0 5 11gt10
• SIM(T4, C1) gt SIM(T4, C2)
• T4 will be added to cluster C1. Now we have the
  following C1 T1, T2, T4 C2 T3
• The new centroid for C1 is now
• C1 lt3/3, 7/3, 3/3, 6/3, 9/3gt

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Step 5

• The only item left unclustered is T5.
• SIM(T5, C1) lt1, 0, 1, 0, 1gt lt3/3, 7/3, 3/3,
  6/3, 9/3gt 3/3 0 3/3 0 9/3 5 lt10
• SIM(T5, C2) lt1, 0, 1, 0, 1gt lt0, 2, 0, 0, 1gt 0
  0 0 0 1 1 lt10
• T5 will have to go into a new cluster C3.

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Final

• The final clusters are
• C1 T1, T2, T4
• C2 T3
• C3 T5

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Note

• The results for this method are highly dependent
  on the similarity threshold.
• The results are also are highly dependent on the
  order of vectors.
• The computation complexity is O(nk), where n is
  the number of vectors and k is the number of
  classes.