论文标题
离散点及其应用的几何配方
Geometric Formulation for Discrete Points and its Applications
论文作者
论文摘要
我们在离散点引入了一种新颖的几何配方。它基于通用微分积分，该计算给出了由函数代数设置的离散的几何描述。我们扩展了这个数学框架，以使其与差异几何形状一致，并在光谱图理论和随机步行方面起作用。因此，我们的配方全面展示了概率理论，物理，应用谐波分析和机器学习中的许多离散框架。我们的方法将表明存在内在理论和这些离散框架的统一图片。
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so that it is consistent with differential geometry, and works on spectral graph theory and random walks. Consequently, our formulation comprehensively demonstrates many discrete frameworks in probability theory, physics, applied harmonic analysis, and machine learning. Our approach would suggest the existence of an intrinsic theory and a unified picture of those discrete frameworks.
