The purpose of this paper is to infer a dynamic graph as a global (collective) model of time-varying measurements at a set of network nodes. This model captures both pairwise as well as higher order interactions (i.e., more than two nodes) among the nodes. The motivation of this work lies in the search for a connectome model which properly captures brain functionality across all regions of the brain, and possibly at individual neurons. We formulate it as an optimization problem, a quadratic objective functional and tensor information of observed node signals over short time intervals. The proper regularization constraints reflect the graph smoothness and other dynamics involving the underlying graph’s Laplacian, as well as the time evolution smoothness of the underlying graph. The resulting joint optimization is solved by a continuous relaxation of the weight parameters and an introduced novel gradient-projection scheme. While the work may be applicable to any time-evolving data set (e.g., fMRI), we apply our algorithm to a real-world dataset comprising recorded activities of individual brain cells. The resulting model is shown to be not only viable but also efficiently computable.

中文翻译：

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动态图学习：一种结构驱动的方法

本文的目的是将动态图推断为一组网络节点上时变测量的全局（集体）模型。该模型捕获节点之间的成对交互以及更高级别的交互（即，两个以上的节点）。这项工作的动机在于寻找一个能够正确捕获大脑所有区域甚至可能单个神经元的大脑功能的连接模型。我们将其表述为一个优化问题，在短时间间隔内观察到的节点信号的二次目标函数和张量信息。适当的正则化约束条件反映了图平滑度和涉及基础图的Laplacian的其他动态，以及基础图的时间演化平滑度。通过连续放宽权重参数和引入的新颖梯度投影方案，解决了最终的联合优化问题。虽然这项工作可能适用于任何随时间变化的数据集（例如fMRI），但我们将我们的算法应用于包含单个脑细胞活动记录的真实数据集。结果表明，该模型不仅可行，而且可有效计算。