Identification of cluster boundary in specified direction

Abstract

The results of a cluster and discriminant analysis are used for the diagnostics of various objects, process control, etc. Not much attention has been given, however, to the presentation, storage, and use of the data analysis results. This pressures users to repeat costly experiments and calculations to solve their application problems. A universal method for presenting and processing the data analysis results is proposed. To do this, the data model presented in our previous works is used. The main component of the model is graphic information with domains in multidimensional space (clusters) bounded by general surfaces. For each boundary there is an error in its description. The boundaries detection error is based on the error of the existing experimental measurements. An algorithm for identifying domains (clusters) in a multidimensional parameter space was proposed and investigated earlier. This paper discusses an algorithm for determining the limit point of the domain (cluster) by a fixed point and a direction vector. Such an algorithm can be used in technological processes to keep parameters within acceptable values, to optimize energy costs when achieving a goal, etc. The paper provides the proof of the algorithm’s correctness, its comparison with an alternative approach and the calculation of computational complexity.