A mathematical approach to seriation

Abstract

We consider the problem of seriating tombs in a cemetery, using only the presence or absence (in each tomb) of objects carrying traits believed to be chronologically significant. This information can be summarized in the form of a matrix A of zeros (indicating absence) and ones (indicating presence), where each row of the matrix is associated with a tomb, and each column with a ‘variety'. A mathemati­cal investigation suggests that much (perhaps all) of the information relevant to seriation is stored in the matrix product AA' , and accordingly this similarity-matrix is taken as the starting-point of a multi­-dimensional scaling procedure. Experiments with artificial data arising from a linear structure show that a two-dimensional output in the form of a horse-shoe is to be expected. If we then read off the labels of the points representing the graves, starting at one ‘vertex' of the horseshoe and working round it till the other is reached, we obtain an estimate of the serial order (or of the serial order reversed).