Paired Patterns in Logical Analysis of Data for Decision Support in Recognition

Logical analysis of data (LAD), an approach to data analysis based on Boolean functions, combinatorics, and optimization, can be considered one of the methods of interpretable machine learning. A feature of LAD is that, among many patterns, different types of patterns can be identified, for example, prime, strong, spanned, and maximum. This paper proposes a decision-support approach to recognition by sharing different types of patterns to improve the quality of recognition in terms of accuracy, interpretability, and validity. An algorithm was developed to search for pairs of strong patterns (prime and spanned) with the same coverage as the training sample, having the smallest (for the prime pattern) and the largest (for the spanned pattern) number of conditions. The proposed approach leads to a decrease in the number of unrecognized observations (compared with the use of spanned patterns only) by 1.5-2 times (experimental results), to some reduction in recognition errors (compared with the use of prime patterns only) of approximately 1% (depending on the dataset) and makes it possible to assess in more detail the level of confidence of the recognition result due to a refined decision-making scheme that uses the information about the number and type of patterns covering the observation.