This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient topological loss. The use of the proposed loss bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations to assess its effectiveness when discriminating networks with different topology. The method is further demonstrated in a twin brain imaging study where we determine if brain networks are genetically heritable. The challenge here is due to the difficulty of overlaying the topologically different functional brain networks obtained from resting-state functional MRI onto the template structural brain network obtained through diffusion MRI.

翻译：本文提出了一种新颖的拓扑学习框架，通过持续同调整合不同规模和拓扑结构的网络。这一具有挑战性的任务因引入了一种计算高效的拓扑损失而得以实现。所提出的损失函数绕过了网络匹配过程中固有的计算瓶颈。我们通过广泛的统计模拟验证了该方法在区分不同拓扑网络时的有效性。该方法进一步在一项双胞胎脑成像研究中得到验证，旨在判断脑网络是否具有遗传性。此处挑战在于，需将通过静息态功能磁共振成像获得的拓扑不同的功能脑网络叠加到通过弥散磁共振成像获取的模板结构脑网络上，这一过程存在较大难度。