Uncovering hidden alignments in two-dimensional point fields

The problem of mapping hidden alignments of points in data sets of two-dimensional points is of significant interest in many geoscience disciplines. In this paper, we revisit this issue and provide a new algorithm, insights, and results. The statistical significance of alignments is assessed by using percentile confidence intervals estimated by a Monte Carlo procedure in which important issues, such as the shape of the geometric support and the possible non-homogeneity of the point density (i.e., clustering effects), have been considered. The procedure is not limited to the simplest case of occurrence and the chance of triads (alignments of three points in a plane) but has been extended to k-ads with k arbitrarily large. The important issue of scale, when searching for point alignments, has also been taken into account. Case studies using synthetic and real data sets are provided to illustrate the methodology and the claims.