Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 7, No 1, (1984), 3p-9p
Abstract:
This paper extends Kendall’s mathematical model of seriation from incidence, or (0, 1) matrices. Given an nxk matrix A, it was established up to now that A'A gives a partial information about the possibility of rearranging A into a P-matrix (i. e. in each column the 1’s are bunched together in a single run). However, according to Kendall, it is AA' which contains sufficient information to decide if A is P-convertible and to construct the row-permutation, which converts A into a P-matrix. The extention considered here is based on both A'A and AA'. A special 3X3 matrix, with pattern called B*, turned out to be very relevant for sériation as well. If there is no submatrix B* in A then both A'A and AA' give sufficient information about the row- and column-permutations, if any, which convert A into an L.-matrix, i. e. all l’s are bunched together in a single block.
