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FAQ. Olli Virmajoki. UNIVERSITY OF JOENSUU DEPARTMENT OF COMPUTER SCIENCE JOENSUU, FINLAND. 11.12.2004. Merge Cost Equation. s i = i th cluster of data vertors s ij = cluster formed by merging i th and j th clusters n i = number of data vectors in s i

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slide1
FAQ

Olli Virmajoki

UNIVERSITY OF JOENSUU

DEPARTMENT OF COMPUTER SCIENCE

JOENSUU, FINLAND

11.12.2004

merge cost equation
Merge Cost Equation
  • si = i th cluster of data vertors
  • sij = cluster formed by merging i th and j th clusters
  • ni = number of data vectors in si
  • nij = numberof data vectors in sij
  • = centroid (mean) of the data vectors in si
  • = centroid (mean) of the data vectors in sij
  • = average squared error between and the data vectors in si
  • = average squared error between and the data vectors in sij
  • = inner product of x and y
exact calculation of the removal cost
Exact calculation of the removal cost
  • Data vectors xi in the cluster sa are divided into subclusters sa,j
  • Removal is conseptually three step process: (1) remove the vectors from the current cluster sa (2) form the subclusters sa,j (3) merge the subclusters to the neighbor clusters sj
removal cost
Removal cost
  • The first term is the cost of the cluster before removal
  • The second term is the sum of the cost values inside the subclusters
  • The third term is the sum of the costs of merging the subclusters sa,jto their neighbor clusters sj
number of clusterings
Number of clusterings
  • M N iterations to cover the search space
  • N distinct vertors to M non-distinct codewords lowers the search by M !
  • Clusterings(N,M)
number of clusterings1
Number of clusterings
  • Consider a number of vectors ordered into groups, one vector at a time
  • Each vector in turn may:
    • Either form a new group on its own, or
    • Combine with other vectors already in a formed group.
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