Lafon Stéphane, Keller Yosi, Coifman Ronald R
Google Inc, Mountain View, CA 94043, USA.
IEEE Trans Pattern Anal Mach Intell. 2006 Nov;28(11):1784-97. doi: 10.1109/TPAMI.2006.223.
Data fusion and multicue data matching are fundamental tasks of high-dimensional data analysis. In this paper, we apply the recently introduced diffusion framework to address these tasks. Our contribution is three-fold: First, we present the Laplace-Beltrami approach for computing density invariant embeddings which are essential for integrating different sources of data. Second, we describe a refinement of the Nyström extension algorithm called "geometric harmonics." We also explain how to use this tool for data assimilation. Finally, we introduce a multicue data matching scheme based on nonlinear spectral graphs alignment. The effectiveness of the presented schemes is validated by applying it to the problems of lipreading and image sequence alignment.
数据融合和多线索数据匹配是高维数据分析的基本任务。在本文中，我们应用最近引入的扩散框架来解决这些任务。我们的贡献有三个方面：第一，我们提出了拉普拉斯 - 贝尔特拉米方法来计算密度不变嵌入，这对于整合不同数据源至关重要。第二，我们描述了一种名为“几何调和”的对奈斯特罗姆扩展算法的改进。我们还解释了如何使用这个工具进行数据同化。最后，我们引入了一种基于非线性谱图对齐的多线索数据匹配方案。通过将其应用于唇读和图像序列对齐问题，验证了所提出方案的有效性。
