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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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FAQ

Olli Virmajoki

UNIVERSITY OF JOENSUU

DEPARTMENT OF COMPUTER SCIENCE

JOENSUU, FINLAND

11.12.2004

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
• 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
• 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
• 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 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.