Abstract The present paper is devoted to clustering geometric graphs. While the standard spectral often not effective for graphs, we an generalization, which call higher-order clustering. It resembles in concept classical method but uses partitioning eigenvector associated with a eigenvalue. We establish weak consistency of this algorithm wide class graphs Soft Geometric Block Model. A small ad...

Spectral clustering (SC) is a popular approach for gaining insights from complex networks. Conventional SC focuses on second-order structures (e.g. edges) without direct consideration of higher-order triangles). This has motivated extensions that directly consider structures. However, both approaches are limited to considering single order. To address this issue, paper proposes novel Mixed-Orde...

Spectral techniques are often used to partition the set of vertices a graph, or form clusters. They based on Laplacian matrix. These allow easily integrate weights edges. In this work, we introduce p-Laplacian, generalized matrix with potential, which also allows us take into account vertices. vertex independent edge weights. way, can cluster importance vertices, assigning more weight some than...

Constrained spectral clustering is a semi-supervised learning problem that aims at incorporating userdefined constraints in spectral clustering. Typically, there are two kinds of constraints: (i) must-link, and (ii) cannot-link. These constraints represent prior knowledge indicating whether two data objects should be in the same cluster or not; thereby aiding in clustering. In this paper, we pr...