Foreseeing the brain evolution as a complex highly inter-connected system, widely modeled as a graph, is crucial for mapping dynamic interactions between different anatomical regions of interest (ROIs) in health and disease. Interestingly, brain graph evolution models remain almost absent in the literature. Here we design an adversarial brain network normalizer for representing each brain network as a transformation of a fixed centered population-driven connectional template. Such graph normalization with respect to a fixed reference paves the way for reliably identifying the most similar training samples (i.e., brain graphs) to the testing sample at baseline timepoint. The testing evolution trajectory will be then spanned by the selected training graphs and their corresponding evolution trajectories. We base our prediction framework on geometric deep learning which naturally operates on graphs and nicely preserves their topological properties. Specifically, we propose the first graph-based Generative Adversarial Network (gGAN) that not only learns how to normalize brain graphs with respect to a fixed connectional brain template (CBT) (i.e., a brain template that selectively captures the most common features across a brain population) but also learns a high-order representation of the brain graphs also called embeddings. We use these embeddings to compute the similarity between training and testing subjects which allows us to pick the closest training subjects at baseline timepoint to predict the evolution of the testing brain graph over time. A series of benchmarks against several comparison methods showed that our proposed method achieved the lowest brain disease evolution prediction error using a single baseline timepoint. Our gGAN code is available at http://github.com/basiralab/gGAN.

中文翻译：

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使用深度对抗网络归一化器预测脑图随时间的演变

将大脑进化预测为一个复杂的、高度互连的系统，广泛建模为图形，对于绘制健康和疾病中不同解剖感兴趣区域 (ROI) 之间的动态相互作用至关重要。有趣的是，文献中几乎没有大脑图进化模型。在这里，我们设计了一个对抗性大脑网络归一化器，用于将每个大脑网络表示为固定中心人口驱动连接模板的转换。这种相对于固定参考的图归一化为在基线时间点可靠地识别与测试样本最相似的训练样本（即脑图）铺平了道路。然后，测试进化轨迹将由选定的训练图及其相应的进化轨迹构成。我们的预测框架基于几何深度学习，几何深度学习自然地对图进行操作并很好地保留了它们的拓扑特性。具体来说，我们提出了第一个基于图的生成对抗网络 (gGAN)，它不仅学习如何相对于固定连接大脑模板 (CBT)（即选择性地捕获最常见特征的大脑模板）对大脑图进行标准化。大脑种群），但也学习大脑图的高阶表示，也称为嵌入。我们使用这些嵌入来计算训练和测试对象之间的相似性，这使我们能够在基线时间点挑选最接近的训练对象，以预测测试大脑图随时间的演变。针对几种比较方法的一系列基准测试表明，我们提出的方法使用单个基线时间点实现了最低的脑疾病进化预测误差。我们的 gGAN 代码可从 http://github.com/basiralab/gGAN 获得。