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Clustering Algorithm Implementation Using Attribute Affinity Matrix

This presentation details the implementation of a clustering algorithm based on a given attribute affinity matrix (AA). It explains the process of transforming AA into a clustered affinity matrix (CA) through iterative selection of optimal placements for attributes. The algorithm focuses on maximizing continuity between attributes, effectively reorganizing the matrix to enhance cluster formation. Key steps include initialization, selecting the "best" attribute placement, and ordering rows based on their relative columns to create a coherent clustered structure.

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Clustering Algorithm Implementation Using Attribute Affinity Matrix

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  1. Distributed Information Systems (CSCI 5533)Presentation ID: 19 Clustering Algorithm Submitted to: Dr. Liaw, Morris Submitted by: Kumar, Manoj

  2. Algorithm 5.3 BEA • Input: AA : attribute affinity matrix • Output: CA : clustered affinity matrix • Begin • { initialize; AA is an nxn matrix} • CA(*,1)← AA(*,1) • CA(*,2)← AA(*,2) • index ← 3 • while index ≤ n do {choose the “best” location for attribute AAindex }

  3. begin for i from 1 to index – 1 by 1 do calculate cont (Ai-1, Aindex, Ai) end-for calculate cont (Aindex-1, Aindex, Aindex+1) loc ← placement given by maximum cont value For j from index to loc by -1 do • CA(*,j)← CA(*,j-1) • end-for

  4. CA(*,loc)← AA(*,index) • index ← index + 1 • end-while • Order the rows according to the relative ordering of columns • end. {BEA}

  5. AM= • AM= • =

  6. bond(Ax,Ay) = • AM= • A1 A2 ……. Ai-1 Ai Aj Aj+1…….. An • AM’ AM’’

  7. AMold = AM’ + AM’’ + bond(Ai-1,Ai) + bond(Ai,Aj) +bond(Aj,Ai) + bond(Aj,Aj+1) • = • + • + 2bond(Ai,Aj)

  8. AMnew = AM’ + AM’’ + bond(Ai,Ak) + bond(Ak,Ai) + bond(Ak,Aj) • + bond(Aj,Ak) • AMnew = AM’ + AM’’ + 2bond(Ai,Ak) + 2bond(Ak,Aj) • Cont(Ai,Ak,Aj) = AMnew – Amold • = 2bond(Ai,Ak) + 2bond(Ak,Aj) - 2bond(Ai,Aj)

  9. Questions ??

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