A method is provided for automatically characterizing data sets containing data points described by d-dimensional vectors obtained by measurements, such as with sonar arrays, as either random or non-random. The data points are located by the d-dimensional vectors in a d-dimensional Euclidean space which may comprise any number d of dimensions and may comprise more than three dimensions. Large or small sets of data may be analyzed. A virtual volume is determined which contains data points from the maximum and minimums of the d-dimensional vectors. The virtual volume is then partitioned. The probability of each partition containing at least one data point for a random distribution is compared to a measurement of the number of partitions actually containing at least one data point whereby the data set is characterized as either random or non-random.