Rank order clustering
Given a binary product-machines n-by-m matrix b_{ip}, rank order clustering is an algorithm characterized by the following steps: • For each row i compute the number \sum_{p=1}^{m}b_{ip}*2^{m-p} • Order rows according to descending numbers previously computed • For each column p compute the number \sum_{i=1}^{n}b_{ip}*2^{n-i} • Order columns according to descending numbers previously computed • If on steps 2 and 4 no reordering happened go to step 6, otherwise go to step 1 • Stop ==Similarity coefficients==
Similarity coefficients
Given a binary product-machines n-by-m matrix, the algorithm proceeds by the following steps: • Compute the similarity coefficient s_{ij}=n_{ij}/(n_{ij}+u) for all with n_{ij} being the number of products that need to be processed on both machine i and machine j, u comprises the number of components which visit machine j but not k and vice versa. • Group together in cell k the tuple (i*,j*) with higher similarity coefficient, with k being the algorithm iteration index • Remove row i* and column j* from the original binary matrix and substitute for the row and column of the cell k, s_{rk}=max(s_{ri*},s_{rj*}) • Go to step 2, iteration index k raised by one Unless this procedure is stopped the algorithm eventually will put all machines in one single group. ==References==