Spectral methods for clustering are now standard, and there are many toy examples in which they can be seen to yield more sensible solutions than classical schemes like vanilla k-means. A more rigorous analysis of these methods has proved elusive, however, and has so far consisted mostly of probabilistic analyses for random inputs with planted clusterings. Such an analysis, typically calls for ...

The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph pLaplacian. Unlike the existing two-node graph Laplacians, this generalization makes it possible to ana...

Principal-component analysis (PCA) has been used for decades to summarize the human genetic variation across geographic regions and to infer population migration history. Reduction of spurious associations due to population structure is crucial for the success of disease association studies. Recently, PCA has also become a popular method for detecting population structure and correction of popu...

This paper studies learning meaningful node representations for signed graphs, where both positive and negative links exist. problem has been widely studied by meticulously designing expressive graph neural networks, as well capturing the structural information of through traditional structure decomposition methods, e.g., spectral theory. In this paper, we propose a novel representation framewo...

The toughness $t(G)$ of a graph $G=(V,E)$ is defined as $t(G)=\min\{\frac{|S|}{c(G-S)}\}$, in which the minimum taken over all $S\subset V$ such that $G-S$ disconnected, where $c(G-S)$ denotes number components $G-S$. We present two tight lower bounds for terms Laplacian eigenvalues and provide strong support conjecture better bound which, if true, implies both bounds, improves generalizes know...

Image deblurring is a relevant problem in many fields of science and engineering. To solve this problem, different approaches have been proposed, and, among the various methods, variational ones are extremely popular. These substitute original with minimization where functional composed two terms, data fidelity term regularization term. In paper we propose, classical non-negative constrained $\...