Clustered Affinity Matrix Calculations
Explore the step-by-step process of calculating clustered affinity matrices, from initializing to re-ordering rows. Follow along with detailed examples and visual representations to understand the calculations better.
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Presentation Transcript
Attribute Affinity Matrix Example A1 A2 A3 A4 A1 A2 A3 A4 q1 q2 q3 q4 A1 A2 A3 A4 45 0 45 0 1 0 1 0 0 80 5 75 0 1 1 0 45 5 53 3 0 1 0 1 0 75 3 78 0 0 1 1 Attribute Usage Matrix Attribute Affinity Matrix (AA) Next Step - Determine clustered affinity (CA)matrix
Clustered Affinity Matrix Step 1: Initialize CA Copy first 2 columns A1 A2 A3 A4 A1 A2 A3 A4 A1 A2 A3 A4 A1 A2 A3 A4 45 0 45 0 45 0 0 80 5 75 0 80 45 5 53 3 45 5 0 75 3 78 0 75 Attribute Affinity Matrix (AA) Clustered Affinity Matrix (CA)
Clustered Affinity Matrix Step 2: Determine Location for A3 3 possible positions for A3 A1 A2 A3 A1 A3 A2 A0 A3 A1 A5 A0 A1 A2 A3 A4 A1 A2 A5 A3 A4 A0 A1 A2 A3 A4 A1 A2 A3 A4 45 0 45 0 45 0 0 80 0 80 5 75 45 5 45 5 53 3 0 75 3 78 0 75 Attribute Affinity Matrix (AA) Clustered Affinity Matrix (CA)
Clustered Affinity Matrix Step 2: Determine the order for A3 n = z = = ( , ) ( , ) ( , ) bond A A aff A A aff A A x y z x z y 1 2 Contribution + ( , , ) ( , ) 2 ( , ) 2 ( , ) cont A A A bond A A bond A A bond A A i k j i k k j i j Cont(A0,A3,A1) = 8820 Cont(A1,A3,A2) = 10150 Cont(A2,A3,A4) = 1780 Since Cont(A1,A3,A2) is the greatest, [A1,A3,A2] is the best order. A1 A2 A3 A4 A1 A3 A2 A4 A1 A2 A3 A4 A1 A2 A3 A4 45 0 45 0 45 45 0 0 80 5 75 0 5 80 45 5 53 3 45 53 5 0 75 3 78 0 3 75 Attribute Affinity Matrix (AA) Clustered Affinity Matrix (CA) Note: aff(A0,Ai)=aff(Ai,A0)=aff(A5,Ai)=aff(Ai,A5)=0 by definition
Clustered Affinity Matrix Step 2: Determine the order for A4 Since Cont(A3,A2,A4) is the biggest, [A3,A2,A4] is the best order. A1 A2 A3 A4 A1 A3 A2 A4 A1 A2 A3 A4 A1 A2 A3 A4 45 0 45 0 45 45 0 0 0 80 5 75 0 5 80 75 45 5 53 3 45 53 5 3 0 75 3 78 0 3 75 78 Attribute Affinity Matrix (AA) Clustered Affinity Matrix (CA)
Clustered Affinity Matrix Step 3: Re-order the Rows The rows are organized in the same order as the columns. A1 A3 A2 A4 A1 A3 A2 A4 A1 A2 A3 A4 A1 A3 A2 A4 45 45 0 0 45 45 0 0 0 5 80 75 45 53 5 3 45 53 5 3 0 5 80 75 0 3 75 78 0 3 75 78 Clustered Affinity Matrix (CA) Clustered Affinity Matrix (CA)
