相关论文: Strong Consistency Guarantees for Clustering High-…

In this study, a novel machine learning algorithm, restricted Boltzmann machine (RBM), is introduced. The algorithm is applied for the spectral classification in astronomy. RBM is a bipartite generative graphical model with two separate…

Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph is generated…

The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that…

Bipartite networks manifest as a stream of edges that represent transactions, e.g., purchases by retail customers. Many machine learning applications employ neighborhood-based measures to characterize the similarity among the nodes, such as…

We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm…

Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…

The stochastic block model (SBM) is a fundamental model for studying graph clustering or community detection in networks. It has received great attention in the last decade and the balanced case, i.e., assuming all clusters have large size,…

The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a…

Community detection is the problem of identifying dense communities in networks. Motivated by transitive behavior in social networks ("thy friend is my friend"), an emerging line of work considers spatially-embedded networks, which…

The spectral bundle method proposed by Helmberg and Rendl is well established for solving large-scale semidefinite programs (SDP) thanks to its low per iteration computational complexity and strong practical performance. In this paper, we…

Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely…

Spectral clustering views the similarity matrix as a weighted graph, and partitions the data by minimizing a graph-cut loss. Since it minimizes the across-cluster similarity, there is no need to model the distribution within each cluster.…

In this paper, we consider the planted partition model, in which $n = ks$ vertices of a random graph are partitioned into $k$ "clusters," each of size $s$. Edges between vertices in the same cluster and different clusters are included with…

Stochastic blockmodels (SBM) and their variants, $e.g.$, mixed-membership and overlapping stochastic blockmodels, are latent variable based generative models for graphs. They have proven to be successful for various tasks, such as…

Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…

The stochastic block model is one of the most studied network models for community detection. It is well-known that most algorithms proposed for fitting the stochastic block model likelihood function cannot scale to large-scale networks.…

Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the number of edges. We introduce the Intersecting Block Graph…

Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…

In Bipartite Correlation Clustering (BCC) we are given a complete bipartite graph $G$ with `+' and `-' edges, and we seek a vertex clustering that maximizes the number of agreements: the number of all `+' edges within clusters plus all `-'…

Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering…