The human brain activity is a popular and important topic in the medical science field and academic studies. In recent years, scientists have been applying various statistical methods to analyze human brain activity. Correlation between brain regions is the most common and fundamental method used to perform this task. However, correlation describes only a two-way relationship. This work explores a new approach by analyzing multi-way relationships. Due to computational complexities, we concentrate on three-way relationships. In particular, we compare conventional two-way correlations and three-way regression models. Data transformed and processed from 3,280 MRI scans of the human brain are used in modeling and analysis. The results of this research show qualified three-way relationships which have a significant advantage relative to their corresponding two-way relationships. The algorithm proposed in this paper can potentially outperform the conventional two-way correlations in exploring the activity of human brain regions.

Library of Congress Subject Headings

Brain--Physiology--Mathematics; Neural circuitry--Mathematics; Neural networks (Neurobiology); Regression analysis; Mathematical statistics

Publication Date


Document Type


Student Type


Degree Name

Applied Statistics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Peter Bajorski

Advisor/Committee Member

Andrew Michael

Advisor/Committee Member

Nathan Cahill


RIT – Main Campus

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