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Summary: We introduce a novel unsupervised approach for the organization and visualization of multidimensional data. At the heart of the method is a presentation of the full pairwise distance matrix of the data points, viewed in pseudocolor. The ordering of points is iteratively permuted in search of a linear ordering, which can be used to study embedded shapes. Several examples indicate how the shapes of certain structures in the data (elongated, circular and compact) manifest themselves visually in our permuted distance matrix. It is important to identify the elongated objects since they are often associated with a set of hidden variables, underlying continuous variation in the data. The problem of determining an optimal linear ordering is shown to be NP-Complete, and therefore an iterative search algorithm with O(n³) step-complexity is suggested. By using sorting points into neighborhoods, i.e. SPIN to …