Given a statistical estimation problem where regularization is performed according to the structure of a large, dense graph G, we consider fitting the statistical estimate using a sparsified surrogate graph G̃, which shares the vertices of G but has far fewer edges, and is thus more tractable to work with computationally. We examine three types of sparsification: spectral sparsification, which c...

In Community question answering (QA) sites, malicious users may provide deceptive answers to promote their products or services. It is important to identify and filter out these deceptive answers. In this paper, we first solve this problem with the traditional supervised learning methods. Two kinds of features, including textual and contextual features, are investigated for this task. We furthe...

This paper investigates the effect of Laplacian normalization in graph-based semi-supervised learning. To this end, we consider multi-class transductive learning on graphs with Laplacian regularization. Generalization bounds are derived using geometric properties of the graph. Specifically, by introducing a definition of graph cut from learning theory, we obtain generalization bounds that depen...

Hyperspectral image (HSI) super-resolution aims at improving the spatial resolution of HSI by fusing a high multispectral (MSI). To preserve local submanifold structures in super-resolution, novel superpixel graph-based method is proposed. Firstly, MSI segmented into blocks to form two-directional feature tensors, then two graphs are created using spectral–spatial distance between unfolded tens...

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

We derive PAC-Bayesian generalization bounds for supervised and unsupervised learning models based on clustering, such as co-clustering, matrix tri-factorization, graphical models, graph clustering, and pairwise clustering.1 We begin with the analysis of co-clustering, which is a widely used approach to the analysis of data matrices. We distinguish among two tasks in matrix data analysis: discr...

in this letter we have proposed a new regularization scheme to deal with the divergent integralsoccurring in the quantum mechanical problem of calculating the bound state energy of the delta-functionpotential in two and three dimensions. based on the schwinger parameterization technique we argue thatthere are no infinities even in d dimensions. in this way we were able to compare our proposal w...

Graph Neural Networks (GNNs) rely on the graph structure to define an aggregation strategy where each node updates its representation by combining information from neighbours. A known limitation of GNNs is that, as number layers increases, gets smoothed and squashed embeddings become indistinguishable, negatively affecting performance. Therefore, practical GNN models employ few only leverage in...

As a powerful model to represent the data, graph has been widely applied to many machine learning tasks. More notably, to address the problems associated with the traditional graph construction methods, sparse representation has been successfully used for graph construction, and one typical work is L1graph. However, since L1-graph often establishes only part of all the valuable connections betw...

Dominant sets are a new graph-theoretic concept that has proven to be relevant in partitional (flat) clustering as well as image segmentation problems. However, in many computer vision applications, such as the organization of an image database, it is important to provide the data to be clustered with a hierarchical organization, and it is not clear how to do this within the dominant set framew...