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This paper investigates the problem of selecting the embedding dimension for large heterogeneous networks that have weakly distinguishable community structure. For a broad family of embeddings based on normalized adjacency matrices, we…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
Sampling techniques such as Respondent-Driven Sampling (RDS) are widely used in epidemiology to sample "hidden" populations, such that properties of the network can be deduced from the sample. We consider how similar techniques can be…
Spectral methods based on the eigenvectors of matrices are widely used in the analysis of network data, particularly for community detection and graph partitioning. Standard methods based on the adjacency matrix and related matrices,…
Community structure analysis is a powerful tool for complex networks, which can simplify their functional analysis considerably. Recently, many approaches were proposed to community structure detection, but few works were focused on the…
We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD…
Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to…
Graph spectra have been successfully used to classify network types, compute the similarity between graphs, and determine the number of communities in a network. For large graphs, where an eigen-decomposition is infeasible, iterative moment…
From the perspective of network analysis, the ubiquitous networks are comprised of regular and irregular components, which makes uncovering the complexity of network structures to be a fundamental challenge. Exploring the regular…
Random graph models are playing an increasingly important role in various fields ranging from social networks, telecommunication systems, to physiologic and biological networks. Within this landscape, the random Kronecker graph model,…
Graph embedding is gaining its popularity for link prediction in complex networks and achieving excellent performance. However, limited work has been done in sparse networks that represent most of real networks. In this paper, we propose a…
Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…
Targeting at depicting land covers with pixel-wise semantic categories, semantic segmentation in remote sensing images needs to portray diverse distributions over vast geographical locations, which is difficult to be achieved by the…
We address the problem of sparse selection of visual features for localizing a team of robots navigating an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most…
A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a…
We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph…
For a large Hermitian matrix $A\in \mathbb{C}^{N\times N}$, it is often the case that the only affordable operation is matrix-vector multiplication. In such case, randomized method is a powerful way to estimate the spectral density (or…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
We aim at accelerating super-resolution (SR) networks on large images (2K-8K). The large images are usually decomposed into small sub-images in practical usages. Based on this processing, we found that different image regions have different…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…