Related papers: Structure-preserving model reduction of physical n…
In this paper, an $\mathscr{H}_2$ norm-based model reduction method for linear quantum systems is presented, which can obtain a physically realizable model with a reduced order for closely approximating the original system. The model…
Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low…
We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…
Visualization of the adjacency matrix enables us to capture macroscopic features of a network when the matrix elements are aligned properly. Community structure, a network consisting of several densely connected components, is a…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multiscale network based approach for the data mining of such structures. The approach is based on…
We study the problem of clustering nodes in a dynamic graph, where the connections between nodes and nodes' cluster memberships may change over time, e.g., due to community migration. We first propose a dynamic stochastic block model that…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…
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…
Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are used to represent ordered relations between entities in the domains. Examples are task…
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…
The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within the frequency region emphasized by the frequency weights. In this paper, we…
This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that…
Clustering trajectory data attracted considerable attention in the last few years. Most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying road network…
This work initiates the study of memory-query tradeoffs for graph problems, with a focus on correlation clustering. Correlation clustering asks for a partition of the vertices that minimizes disagreements: non-edges inside clusters plus…
Classifying whole images is a classic problem in machine learning, and graph neural networks are a powerful methodology to learn highly irregular geometries. It is often the case that certain parts of a point cloud are more important than…
We give the first $2$-approximation algorithm for the cluster vertex deletion problem. This is tight, since approximating the problem within any constant factor smaller than $2$ is UGC-hard. Our algorithm combines the previous approaches,…
The large size of multiscale, distribution and transmission, power grids hinder fast system-wide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable…
Until recently obtaining data on populations of networks was typically rare. However, with the advancement of automatic monitoring devices and the growing social and scientific interest in networks, such data has become more widely…