论文标题
图形拉普拉斯人，里曼尼亚语歧管及其机器学习
Graph Laplacians, Riemannian Manifolds and their Machine-Learning
论文作者
论文摘要
图形拉普拉斯主义者以及相关的光谱不平等和（共同的同源性）提供了分散的riemannian歧管类似物，从而在组合，几何学和理论物理学之间提供了丰富的相互作用。我们将一些最新技术应用于数据科学中的一些技术，例如监督和无监督的机器学习和拓扑数据分析，鉴于研究这些对应关系，大约8000个有限图的Wolfram数据库。令人鼓舞的是，我们发现神经分类器，回归器和网络可以高效而准确地执行，从识别图形静电性到预测频谱差距到检测汉密尔顿周期的存在等多种任务等。
Graph Laplacians as well as related spectral inequalities and (co-)homology provide a foray into discrete analogues of Riemannian manifolds, providing a rich interplay between combinatorics, geometry and theoretical physics. We apply some of the latest techniques in data science such as supervised and unsupervised machine-learning and topological data analysis to the Wolfram database of some 8000 finite graphs in light of studying these correspondences. Encouragingly, we find that neural classifiers, regressors and networks can perform, with high efficiently and accuracy, a multitude of tasks ranging from recognizing graph Ricci-flatness, to predicting the spectral gap, to detecting the presence of Hamiltonian cycles, etc.
