Using interpoint distances for pattern recognition
Alexander M. Shurygin · Pattern Recognition and Image Analysis · 2006
The simplest problem of pattern recognition is considered, viz., recognition of two classes of objects given by points in Euclidean space; the recognition is fulfilled using the fraction of samples that fall within a ball of radius r with the center at the specified point. The interpoint distances are considered both within the totalities and between them. Their pairwise asymptotic independence is proved, which allows reducing the multidimensional distribution to one-dimensional, where simple yet important problems can be solved. For instance, one can check the significance of the difference between the class distributions, choose the optimal value of radius r , and stably estimate the error of recognition.