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Principal component analysis (PCA) is a foundational tool in modern data analysis, and a crucial step in PCA is selecting the number of components to keep. However, classical selection methods (e.g., scree plots, parallel analysis, etc.)…
Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and…
An overarching objective in contemporary statistical network analysis is extracting salient information from datasets consisting of multiple networks. To date, considerable attention has been devoted to node and network clustering, while…
Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the…
Network embedding, a graph representation learning method illustrating network topology by mapping nodes into lower-dimension vectors, is challenging to accommodate the ever-changing dynamic graphs in practice. Existing research is mainly…
In this paper, we propose to estimate the invariant subspace across heterogeneous multiple networks using a novel bias-corrected joint spectral embedding algorithm. The proposed algorithm recursively calibrates the diagonal bias of the sum…
Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…
We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on…
Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a…
Most of the real world complex networks such as the Internet, World Wide Web and collaboration networks are huge; and to infer their structure and dynamics one requires handling large connectivity (adjacency) matrices. Also, to find out the…
While several feature embedding models have been developed in the literature, comparisons of these embeddings have largely focused on their numerical performance in classification-related downstream applications. However, an interpretable…
Community detection in multi-layer networks has emerged as a crucial area of modern network analysis. However, conventional approaches often assume that nodes belong exclusively to a single community, which fails to capture the complex…
Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to…
As network data has become ubiquitous in the sciences, there has been growing interest in network models whose structure is driven by latent node-level variables in a (typically low-dimensional) latent geometric space. These "latent…
Attributed networks are ubiquitous since a network often comes with auxiliary attribute information e.g. a social network with user profiles. Attributed Network Embedding (ANE) has recently attracted considerable attention, which aims to…
Given a set of k networks, possibly with different sizes and no overlaps in nodes or edges, how can we quickly assess similarity between them, without solving the node-correspondence problem? Analogously, how can we extract a small number…
We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or…
This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random…