This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the Markov Variation minimization problem. The paper showcases the effectiveness of this approach through examples involving synthetically generated and real-world temperature sensor data. These examples also compare the diffusion map graph signal model with other commonly used graph signal operators. The results provide new approaches for the analysis and understanding of complex, non-Euclidean data structures.

翻译：本文探讨了将扩散映射作为图位移算子，用于理解图信号底层几何结构的应用。研究评估了在马尔可夫变分最小化问题中，使用扩散映射生成滤波器对图学习性能的提升效果。通过合成数据与真实温度传感器数据案例，展示了该方法的有效性，并与常用图信号算子进行对比。研究结果为复杂非欧几里得数据结构的分析与理解提供了新思路。