A Study of Robust Partial Correlation between Electroencephalogram Connectivity and Human Arithmetic Abilities

• Published in: Pattern recognition and image analysis Vol. 35; no. 2; pp. 189 - 200
• Main Authors: Timofeeva, Anastasiia Yurievna, Avdeenko, Tatiana Vladimirovna, Alkov, Sergei Sergeevich
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.06.2025; Springer Nature B.V
• Subjects: 2024; Arithmetical ability; Brain; Coherence; Computation; Computer Science; Connectivity; Correlation coefficients; Electroencephalography; Frequency ranges; Graph theory; Human performance; Image Processing and Computer Vision; Mathematical analysis; NIZHNY NOVGOROD; Pattern Recognition; Phase lag; Robustness; RUSSIAN FEDERATION; Selected Conference Papers; Synchronism; XXVI INTERNATIONAL CONFERENCE DAMDID/RCDL-2024 OCTOBER 23–25; arithmetic abilities; robustness; partial correlation; connectivity; graph metrics; electroencephalogram
• ISSN: 1054-6618; 1555-6212
• DOI: 10.1134/S1054661825700105

Numerous studies of human brain activation patterns based on electroencephalogram data show contradictory results. Therefore, the search for and analysis of methods that allow identifying stable correlations of these patterns with the characteristics and states of subjects, their cognitive abilities, and types and schemes of experiments is an extremely urgent task. The present study focuses on the search for features obtained from electroencephalogram data that robust correlate with human arithmetic abilities. The elements of the initial set from which the subset of informative features is extracted are the metrics of the graph constructed using five methods of computing the connectivity matrix, which characterize in different ways the degree of spatial synchronization of electroencephalogram signals (coherence, imaginary coherence, phase lag index, directed phase lag index, weighted phase lag index), which were calculated in five frequency ranges (delta, theta, alpha, beta, gamma). For each method of computing the connectivity matrix and each frequency range, a connectivity graph is constructed, which is determined by pairs of significant interactions between areas of the brain, and then, for each such graph, seven connectivity metrics are calculated, ultimately forming a set of 5 × 5 × 7 = 175 initial features. The studies are repeated for different values of the thresholds of significance of interaction of channels when constructing connectivity graphs. With this issue formulation, the problem of multicollinearity of graph metrics arises, which does not allow obtaining stable results. To solve it, the paper proposes an approach the essence of which is to select a feature with the highest absolute value of the rank partial correlation coefficient, then construct a regression of this feature on the remaining variables, and use the coefficients of this regression to form a common factor. The results showed that the use of a partial correlation coefficient makes it possible not only to select more significant metrics of the connectivity graph but also to identify hidden connections with the target feature of arithmetic abilities that cannot be detected using paired correlations because of the presence of multicollinearity of features.