Reviews: Topological Distances and Losses for Brain Networks
Reviews: Topological Distances and Losses for Brain Networks
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发表时间：
2021-02
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通讯作者：
M. Chung;Alexander D. Smith;G. Shiu
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作者：
M. Chung;Alexander D. Smith;G. Shiu
几乎所有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函数，这些函数大多是欧几里得或矩阵范数。欧几里得距离或矩阵距离可能无法捕捉大脑网络中潜在的微妙拓扑差异。此外，欧几里德距离对异常值很敏感。一些极端的边缘权重可能会严重影响距离。因此，有必要使用识别数据拓扑的距离和损失函数。在这篇综述论文中，我们调查了拓扑数据分析（TDA）和持久同源性中的各种拓扑距离和损失函数，可以更有效地用于脑网络分析。尽管最近有很多基于TDA方法的脑成像研究，但可能由于缺乏方法意识，TDA尚未成为脑成像领域的主流工具。本文的主要目的是提供这些立即适用于脑网络数据的强大工具的相关技术调查。
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.