Related papers: Large sample spectral analysis of graph-based mult…
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…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
For data represented by networks, the community structure of the underlying graph is of great interest. A classical clustering problem is to uncover the overall ``best'' partition of nodes in communities. Here, a more elaborate description…
We design new parallel algorithms for clustering in high-dimensional Euclidean spaces. These algorithms run in the Massively Parallel Computation (MPC) model, and are fully scalable, meaning that the local memory in each machine may be…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
Spectral clustering is discussed from many perspectives, by extending it to rectangular arrays and discrepancy minimization too. Near optimal clusters are obtained with singular value decomposition and with the weighted $k$-means algorithm.…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale parallel computation frameworks and has recently gained a lot of importance, especially in the context of classic graph problems.…
The Minimum Consistent Subset (MCS) problem arises naturally in the context of supervised clustering and instance selection. In supervised clustering, one aims to infer a meaningful partitioning of data using a small labeled subset.…
Multilayer graph has garnered plenty of research attention in many areas due to their high utility in modeling interdependent systems. However, clustering of multilayer graph, which aims at dividing the graph nodes into categories or…
Despite the impressive clustering performance and efficiency in characterizing both the relationship between data and cluster structure, existing graph-based multi-view clustering methods still have the following drawbacks. They suffer from…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…
Spectral clustering is a popular algorithm that clusters points using the eigenvalues and eigenvectors of Laplacian matrices derived from the data. For years, spectral clustering has been working mysteriously. This paper explains spectral…
Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized…
We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…
Multimodal graphs, which integrate unstructured heterogeneous data with structured interconnections, offer substantial real-world utility but remain insufficiently explored in unsupervised learning. In this work, we initiate the study of…
Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. Constructing precise and local kernel matrices is proved to be of vital significance in applications since the unreliable…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
Maximal Clique Enumeration (MCE) is a fundamental graph mining problem, and is useful as a primitive in identifying dense structures in a graph. Due to the high computational cost of MCE, parallel methods are imperative for dealing with…