Reviews: Topological Distances and Losses for Brain Networks

Abstract

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.

References in corpus (12)

• A roadmap for the computation of persistent homology
• Statistical topological data analysis using persistence landscapes
• Adversarial Attacks and Defences: A Survey
• Topological strata of weighted complex networks
• Brain Network Adaptability Across Task States
• Persistent homology of time-dependent functional networks constructed from coupled time series
• On the stability of persistent entropy and new summary functions for TDA
• The persistence landscape and some of its properties
• A Topological Regularizer for Classifiers via Persistent Homology
• The Persistence of Large Scale Structures I: Primordial non-Gaussianity
• Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
• Autism Spectrum Disorder Classification using Graph Kernels on Multidimensional Time Series