相关论文: Multiway $p$-spectral graph cuts on Grassmann mani…

Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…

Choosing a meaningful subset of features from high-dimensional observations in unsupervised settings can greatly enhance the accuracy of downstream analysis, such as clustering or dimensionality reduction, and provide valuable insights into…

Network-valued data are encountered in a wide range of applications and pose challenges in learning due to their complex structure and absence of vertex correspondence. Typical examples of such problems include classification or grouping of…

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…

We introduce a novel hybrid quantum-analog algorithm to perform graph clustering that exploits connections between the evolution of dynamical systems on graphs and the underlying graph spectra. This approach constitutes a new class of…

Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach…

A popular graph clustering method is to consider the embedding of an input graph into R^k induced by the first k eigenvectors of its Laplacian, and to partition the graph via geometric manipulations on the resulting metric space. Despite…

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative…

Graph signal processing (GSP) studies signals that live on irregular data kernels described by graphs. One fundamental problem in GSP is sampling---from which subset of graph nodes to collect samples in order to reconstruct a bandlimited…

This manuscript studies nodal clustering in graphs having multivariate attributes at each node. The framework includes node-specific priors for low-dimensional representations, coupled with a neural decoder that bridges observed attributes…

Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…

We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several…

Recently, manifold regularized semi-supervised learning (MRSSL) received considerable attention because it successfully exploits the geometry of the intrinsic data probability distribution including both labeled and unlabeled samples to…

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect…

Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a…

In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously,…

Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously…

UMAP (Uniform Manifold Approximation and Projection) is among the most widely used algorithms for non linear dimensionality reduction and data visualisation. Despite its popularity, and despite being presented through the lens of algebraic…

Spectral clustering is one of the most popular clustering methods for finding clusters in a graph, which has found many applications in data mining. However, the input graph in those applications may have many missing edges due to error in…

In this paper, we cast the scribble-based interactive image segmentation as a semi-supervised learning problem. Our novel approach alleviates the need to solve an expensive generalized eigenvector problem by approximating the eigenvectors…