Determination of centroids to increase the accuracy of ordinal-invariant pattern clustering

The work continues the research of constructing methods for analyzing patterns in parallel coordinates independent of the sequence of input data of the results. The basic operations on objects of ordinal-invariant pattern clusters are described. The assertion that the centroid of an ordinal-invariant pattern cluster belongs to the original cluster is proved, which allows one to estimate the intracluster object - centroid distances in the multidimensional feature space. Examples of revealing the structural similarity of objects in parallel coordinates are given. The main differences between the methods of analysis of patterns and cluster analysis are noted. The methodology of the centroid detection of the ordinal-invariant pattern-cluster is described. An algorithm for combining groups of objects based on their structural similarity, on the one hand, and minimizing intracluster distances, on the other, is proposed, which makes it possible to improve the accuracy of the final results and partially solve the problem of finding similar objects in the presence of error in the original data. The proposed algorithm uses the concept of intracluster distances “object - centroid” and satisfies the following conditions: endogenous determination of the number and composition of the desired groups of objects under study; low (relatively) computational complexity; independence of the original partition from the initial sequence of input data. The work of the proposed algorithm on classical data sets is demonstrated. The results of testing are presented and the clustering accuracy is increased.