Making Laplacians commute

Abstract

In this paper, we construct multimodal spectral geometry by finding a pair of closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are jointly diagonalizable and hence have the same eigenbasis. Our construction 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 applications in dimensionality reduction, shape analysis, and clustering, demonstrating that our method better captures the inherent structure of multi-modal data.

References in corpus (4)

• Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds
• Learning Multi-modal Similarity
• Multimodal diffusion geometry by joint diagonalization of Laplacians
• Almost-commuting matrices are almost jointly diagonalizable

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• Structure-preserving color transformations using Laplacian commutativity