Related papers: Hypergraphs with Edge-Dependent Vertex Weights: Sp…
Multilayer graphs encode different kind of interactions between the same set of entities. When one wants to cluster such a multilayer graph, the natural question arises how one should merge the information different layers. We introduce in…
The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…
In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that…
This paper is concerned with the controllability problem of a connected threshold graph following the Laplacian dynamics. An algorithm is proposed to generate a spanning set of orthogonal Laplacian eigenvectors of the graph from a…
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…
Hyperspectral image classification (HIC) is an important but challenging task, and a problem that limits the algorithmic development in this field is that the ground truths of hyperspectral images (HSIs) are extremely hard to obtain.…
A hypergraph is a data structure composed of nodes and hyperedges, where each hyperedge is an any-sized subset of nodes. Due to the flexibility in hyperedge size, hypergraphs represent group interactions (e.g., co-authorship by more than…
In this paper we consider the problem of transmission across a graph and how to effectively control/restrict it with limited resources. Transmission can represent information transfer across a social network, spread of a malicious virus…
Hypergraphs are a useful abstraction for modeling multiway relationships in data, and hypergraph clustering is the task of detecting groups of closely related nodes in such data. Graph clustering has been studied extensively, and there are…
The K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. However, it combines the K-means clustering and dimensionality reduction processes for…
We report our experiments in identifying large bipartite subgraphs of simple connected graphs which are based on the sign pattern of eigenvectors belonging to the extremal eigenvalues of different graph matrices: adjacency, signless…
We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured in many different metrics. For instance similarity between two papers can be based on common authors, where…
Spectral graph sparsification has emerged as a powerful tool in the analysis of large-scale networks by reducing the overall number of edges, while maintaining a comparable graph Laplacian matrix. In this paper, we present an efficient…
Current graph clustering methods emphasize individual node and edge con nections, while ignoring higher-order organization at the level of motif. Re cently, higher-order graph clustering approaches have been designed by motif based…
Network data appears in very diverse applications, like biological, social, or sensor networks. Clustering of network nodes into categories or communities has thus become a very common task in machine learning and data mining. Network data…
We consider a framework for clustering edge-colored hypergraphs, where the goal is to cluster (equivalently, to color) objects based on the primary type of multiway interactions they participate in. One well-studied objective is to color…
This work studies the classical spectral clustering algorithm which embeds the vertices of some graph $G=(V_G, E_G)$ into $\mathbb{R}^k$ using $k$ eigenvectors of some matrix of $G$, and applies $k$-means to partition $V_G$ into $k$…
Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…
Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…
In this study, we explore the interrelation between hypergraph symmetries represented by equivalence relations on the vertex set and the spectra of operators associated with the hypergraph. We introduce the idea of equivalence relation…