Distributed Information Systems (CSCI 5533)

Presentation ID: 19

Clustering Algorithm

Submitted to: Dr. Liaw, Morris

Submitted by: Kumar, Manoj

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 }

beginfor i from 1 to index – 1 by 1 do calculate cont (Ai-1, Aindex, Ai)end-forcalculate cont (Aindex-1, Aindex, Aindex+1)loc ← placement given by maximum cont valueFor j from index to loc by -1 do• CA(*,j)← CA(*,j-1)• end-for

• CA(*,loc)← AA(*,index)• index ← index + 1• end-while• Order the rows according to the relative ordering

of columns• end. {BEA}

• AM=

• AM=

• = ),(),(),(),( 11

111

jiji

n

ijij

n

ii

n

j

AAaffAAaffAAaffAAaff

)],(),(),(),([ 1111

jijijij

n

ji

n

i

AAaffAAaffAAaffAAaff

)],(),()[,( 1111

jijij

n

ji

n

i

AAaffAAaffAAaff

• bond(Ax,Ay) =

• AM=

• A1 A2 ……. Ai-1 Ai Aj Aj+1…….. An• AM’ AM’’

)],(),([ 111

jjj

n

jj AAbondAAbond

),(),(1

yzx

n

zz AAaffAAaff

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

• =

• +

• + 2bond(Ai,Aj)

)],(),([ 111

lll

n

ll AAbondAAbond

)],(),([ 112

lll

n

ill AAbondAAbond

• 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)

• Questions ??