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01/02/20031 Global affinity measure: GAM = aff(A i, A j )*[aff(A i, A j-1 ) + aff(A i, A j+1 ) + aff(A i-1, A j ) + aff(A i+1, A j )] Since the affinity matrix is symmetric, we have GAM = 2 *aff(A i, A j )*[aff(A i, A j-1 ) + aff(A i, A j+1 )] AM = aff(A i, A j )*[aff(A i, A j-1 ) + aff(A i, A j+1 )]

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01/02/20032 Global affinity measure: AM = aff(A i, A j )*[aff(A i, A j-1 ) + aff(A i, A j+1 )] = [aff(A i, A j )*aff(A i, A j-1 ) + aff(A i, A j )*aff(A i, A j+1 )] = [bond(A i, A j-1 ) + bond(A i, A j+1 )], Where bond(A x, A y ) = aff(A z, A x )*aff(A z, A y ).

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01/02/20033 Relation schema: R[A 1, …, A i, …, A j, …, A k-1, A k, …, A n ] Affinity matrix: A 1, …, A i, …, A j, …, A k-1, A k, …, A n … … … … … Clustered affinity matrix: A i1, …, A il, A i, A j, A i(l+3), …, A i(k-1) A i1, …, A il, A i, A k, A j, A i(l+3), …, … ……… …… old new

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01/02/20034 AM old = AM old = [bond(A is, A i(s-1) ) + bond(A is, A j(s+1) )] + bond(A i, A il ) + bond(A i, A j ) + bond(A j, A i ) + bond(A j, A i(l+3) ) + [bond(A is, A i(s-1) ) + bond(A is, A j(s+1) )] AM new = AM new = [bond(A is, A i(s-1) ) + bond(A is, A j(s+1) )] + bond(A i, A il ) + bond(A i, A k ) + bond(A k, A i ) + bond(A k, A j ) + bond(A j, A k ) + bond(A j, A i(l+3) ) + [bond(A is, A i(s-1) ) + bond(A is, A j(s+1) )] AM new AM old = 2* AM new – AM old = 2* bond(A i, A k ) + 2* bond(A j, A k ) – 2* bond(A i, A j )

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