Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle topological differences in brain networks. Further, Euclidean distances are sensitive to outliers. A few extreme edge weights may severely affect the distance. Thus it is necessary to use distances and loss functions that recognize topology of data. In this review paper, we survey various topological distance and loss functions from topological data analysis (TDA) and persistent homology that can be used in brain network analysis more effectively. Although there are many recent brain imaging studies that are based on TDA methods, possibly due to the lack of method awareness, TDA has not taken as the mainstream tool in brain imaging field yet. The main purpose of this paper is provide the relevant technical survey of these powerful tools that are immediately applicable to brain network data.
翻译:几乎所有用于分析大脑网络的统计和机器学习方法都依赖于距离和损失功能,这些功能大多是Euclidean或矩阵规范。欧洲人或矩阵距离可能无法捕捉到大脑网络中潜在的微妙的地形差异。此外,欧洲人距离对离子很敏感。一些极端边缘重量可能严重影响距离。因此有必要使用认识数据地形的距离和损失功能。在本审查文件中,我们调查了可更有效地用于脑网络分析的各种地貌数据分析(TDA)和持久性同系物的地形距离和损失功能。虽然最近有许多基于TDA方法的脑成像研究,但可能由于对方法缺乏认识,TDA尚未被作为大脑成像领域的主流工具。本文的主要目的是提供这些直接适用于脑网络数据的强大工具的相关技术调查。