基于Laplacian算子联合对角化的多峰扩散几何
Multimodal diffusion geometry by joint diagonalization of Laplacians
摘要：
我们通过拉普拉斯矩阵的联合近似对角化构造了扩散几何到多模态的扩展。这自然扩展了基于谱几何的经典数据分析工具，如扩散图和谱聚类。我们提供了几个流形学习，检索和聚类的合成和真实的例子，证明联合扩散几何经常更好地捕捉多模态数据的固有结构。我们还表明，许多以前的尝试，构建多模态谱聚类可以被看作是联合近似对角化的拉普拉斯算子的特殊情况。
英文摘要：
We construct an extension of diffusion geometry to multiple modalities through joint approximate diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, retrieval, and clustering demonstrating that the joint diffusion geometry frequently better captures the inherent structure of multi-modal data. We also show that many previous attempts to construct multimodal spectral clustering can be seen as particular cases of joint approximate diagonalization of the Laplacians.
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