arXiv:2502.14878q-bio.NCcs.LG2025-02

用随机矩阵理论识别脑功能区关联,提升疾病检测可靠性。

Applications of Random Matrix Theory in Machine Learning and Brain Mapping

  • 基于随机矩阵理论分析fMRI数据中的脑区关联
  • 无论加何种噪声,特征值分布均趋近理论预测
  • 可发现新脑网络,适合神经科学与医疗AI研究者

脑成像通过分析脑信号波长生成图像,由放射科医生解读。引入机器学习可减少人为误差并提升效率。关键挑战在于以体素为单位确定脑功能区间的相关性,从而判断脑功能状态并用于疾病、残疾和病症的检测。然而,随机噪声干扰真实信号的识别。本文探讨了随机矩阵理论(RMT)算法在机器学习中的应用,用于检测脑功能区间的相关性。通过模拟不同刺激下各时间点的体素信号强度,构建威沙特矩阵(Wishart Matrices),并利用马尔琴科-帕斯图定律(Marchenko-Pastur law)进行分析。结果表明,无论添加何种噪声,观测到的特征值分布始终收敛至理论分布,说明RMT具有高稳健性和测试-重测可靠性。这表明特征值间存在强相关性,反映脑功能区域的内在连接。显著偏离理论预测的特征值可能提示新离散脑网络的发现。

原文摘要 · Abstract (English)

Brain mapping analyzes the wavelengths of brain signals and outputs them in a map, which is then analyzed by a radiologist. Introducing Machine Learning (ML) into the brain mapping process reduces the variable of human error in reading such maps and increases efficiency. A key area of interest is determining the correlation between the functional areas of the brain on a voxel (3-dimensional pixel) wise basis. This leads to determining how a brain is functioning and can be used to detect diseases, disabilities, and sicknesses. As such, random noise presents a challenge in consistently determining the actual signals from the scan. This paper discusses how an algorithm created by Random Matrix Theory (RMT) can be used as a tool for ML, as it detects the correlation of the functional areas of the brain. Random matrices are simulated to represent the voxel signal intensity strength for each time interval where a stimulus is presented in an fMRI scan. Using the Marchenko-Pastur law for Wishart Matrices, a result of RMT, it was found that no matter what type of noise was added to the random matrices, the observed eigenvalue distribution of the Wishart Matrices would converge to the theoretical distribution. This means that RMT is robust and has a high test-re-test reliability. These results further indicate that a strong correlation exists between the eigenvalues, and hence the functional regions of the brain. Any eigenvalue that differs significantly from those predicted from RMT may indicate the discovery of a new discrete brain network.

脑科学随机矩阵fMRI分析机器学习

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