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Article

Low-Rank Approximation of Difference between Correlation Matrices Using Inner Product

Department of Biomedical Sciences and Informatics, Doshisha University, Kyoto 602-8580, Japan
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Appl. Sci. 2021, 11(10), 4582; https://doi.org/10.3390/app11104582
Received: 30 March 2021 / Revised: 13 May 2021 / Accepted: 14 May 2021 / Published: 17 May 2021
(This article belongs to the Section Applied Biosciences and Bioengineering)
In the domain of functional magnetic resonance imaging (fMRI) data analysis, given two correlation matrices between regions of interest (ROIs) for the same subject, it is important to reveal relatively large differences to ensure accurate interpretation. However, clustering results based only on differences tend to be unsatisfactory and interpreting the features tends to be difficult because the differences likely suffer from noise. Therefore, to overcome these problems, we propose a new approach for dimensional reduction clustering. Methods: Our proposed dimensional reduction clustering approach consists of low-rank approximation and a clustering algorithm. The low-rank matrix, which reflects the difference, is estimated from the inner product of the difference matrix, not only from the difference. In addition, the low-rank matrix is calculated based on the majorize–minimization (MM) algorithm such that the difference is bounded within the range 1 to 1. For the clustering process, ordinal k-means is applied to the estimated low-rank matrix, which emphasizes the clustering structure. Results: Numerical simulations show that, compared with other approaches that are based only on differences, the proposed method provides superior performance in recovering the true clustering structure. Moreover, as demonstrated through a real-data example of brain activity measured via fMRI during the performance of a working memory task, the proposed method can visually provide interpretable community structures consisting of well-known brain functional networks, which can be associated with the human working memory system. Conclusions: The proposed dimensional reduction clustering approach is a very useful tool for revealing and interpreting the differences between correlation matrices, even when the true differences tend to be relatively small. View Full-Text
Keywords: k-means; fMRI data analysis; MM algorithm k-means; fMRI data analysis; MM algorithm
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MDPI and ACS Style

Tanioka, K.; Hiwa, S. Low-Rank Approximation of Difference between Correlation Matrices Using Inner Product. Appl. Sci. 2021, 11, 4582. https://doi.org/10.3390/app11104582

AMA Style

Tanioka K, Hiwa S. Low-Rank Approximation of Difference between Correlation Matrices Using Inner Product. Applied Sciences. 2021; 11(10):4582. https://doi.org/10.3390/app11104582

Chicago/Turabian Style

Tanioka, Kensuke, and Satoru Hiwa. 2021. "Low-Rank Approximation of Difference between Correlation Matrices Using Inner Product" Applied Sciences 11, no. 10: 4582. https://doi.org/10.3390/app11104582

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