Title: Applications of Random Matrix Theory in Machine Learning and Brain Mapping Show Chinese title

Title: 随机矩阵理论在机器学习和脑图谱中的应用

Abstract: 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. Show Chinese abstract

Abstract: 脑图分析脑信号的波长，并将其输出为地图，然后由放射科医生进行分析。 将机器学习（ML）引入脑图过程可以减少在阅读此类地图时的人为错误变量，并提高效率。 一个感兴趣的关键领域是确定脑功能区域在体素（三维像素）基础上的相关性。 这有助于确定大脑的功能，并可用于检测疾病、残疾和病症。 因此，随机噪声在一致确定扫描中的实际信号方面构成了挑战。 本文讨论了由随机矩阵理论（RMT）创建的算法如何作为机器学习的工具，因为它可以检测脑功能区域的相关性。 随机矩阵被模拟以表示在fMRI扫描中呈现刺激的每个时间间隔的体素信号强度。 使用Wishart矩阵的Marchenko-Pastur定律，这是RMT的一个结果，发现无论向随机矩阵添加何种类型的噪声，观察到的Wishart矩阵特征值分布都会收敛到理论分布。 这意味着RMT具有鲁棒性，并且具有很高的测试-再测试可靠性。 这些结果进一步表明，特征值之间存在强相关性，因此脑功能区域之间也存在强相关性。 任何与RMT预测显著不同的特征值可能表明发现了新的离散脑网络。