Multidimensional dot-matrices.

A generalization of the dot-matrix of similarity for n sequences is proposed. For the visualization of the n-dimensional dot-matrix, the n projections onto the plane passing through the main diagonal and each of the n axes of Euclidean space En are displayed. The projection is compressed so that the points at the coordinates (xi, sigma j not equal to ixj/(n - 1)) are depicted on the plane. The common regions of similarity are revealed as segments of straight lines parallel to the main diagonal. An algorithm for the n-dimensional dot-matrix calculation of time of the order of O[nL2 + n(L2p)2] is suggested where L is the mean length of sequence and p is the stringency parameter of the order of 10(-6). The method is illustrated for the family of plant phenylalanine ammonia-lyase genes.