Informatics and Applications

2026, Volume 20, Issue 3, pp 87-95

METHODS FOR GENERATING METRICS ON OBJECT SETS IN THE CONTEXT OF TOPOLOGICAL DATA ANALYSIS THEORY. PART 2. EXPERIMENTAL GENERATION OF METRICS ON OBJECTS IN THE CONTEXT OF METRIC ALGORITHMS FOR NUMERICAL FORECASTING

  • I. Yu. Torshin

Abstract

In the first part of this work, the main theoretical directions for generating problem-oriented metrics on sets of objects (pQ-metrics) using metrics on features (pL-metrics) were systematized. In this paper, criteria for tuning PQ-metrics are obtained using concepts of compactness. Computational experiments were conducted on 1000 independent data samples with 5000 pQ-metrics synthesized according to 20 proposed approaches for numerical forecasting by fc-nearest neighbor algorithms. Computational experiments demonstrated that in 95% cases, pQ-metrics of three types were effective: (i) those based on synthetic numerical features (61%); (ii) vector- based with pairwise matching (22%); and (iii) noncommutative metrics based on pL-distance arrays (12%). Importantly, pQ-metrics based on synthetic numerical features provided the best result for 83% of the datasets, which makes this approach the most promising.

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