The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs.
NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms that iteratively solves alternating non-negative least squares (NLS) subproblems for $W$ and $H$.
Although many methods exist, the No Free Lunch theorem for community detection implies that each makes some kind of tradeoff, and no algorithm can be optimal on all inputs. These results introduce both a theoretically principled approach to evaluate over and underfitting in models of network community structure and a realistic benchmark by which new methods may be evaluated and compared.
In this paper, we propose CommunityGAN, a novel community detection framework that jointly solves overlapping community detection and graph representation learning. First, unlike the embedding of conventional graph representation learning algorithms where the vector entry values have no specific meanings, the embedding of CommunityGAN indicates the membership strength of vertices to communities.
Network embedding methodologies, which learn a distributed vector representation for each vertex in a network, have attracted considerable interest in recent years. For a given network, Neural-Brane extracts latent feature representation of its vertices using a designed neural network model that unifies network topological information and nodal attributes; Besides, it utilizes Bayesian personalized ranking objective, which exploits the proximity ordering between a similar node-pair and a dissimilar node-pair.
Although various approaches have been proposed to compute node embeddings, many successful methods benefit from random walks in order to transform a given network into a collection of sequences of nodes and then they target to learn the representation of nodes by predicting the context of each vertex within the sequence. Similar to the notion of topical word embeddings in NLP, the proposed method assigns each vertex to a topic with the favor of various statistical models and community detection methods, and then generates the enhanced community representations.
Recent successes in word embedding and document embedding have motivated researchers to explore similar representations for networks and to use such representations for tasks such as edge prediction, node label prediction, and community detection. Such network embedding methods are largely focused on finding distributed representations for unsigned networks and are unable to discover embeddings that respect polarities inherent in edges.
Network embedding algorithms are able to learn latent feature representations of nodes, transforming networks into lower dimensional vector representations. We have performed a detailed experimental evaluation comparing the performance of the proposed algorithm against various baseline methods, on several datasets and learning tasks.
Although the computational and statistical trade-off for modeling single graphs, for instance, using block models is relatively well understood, extending such results to sequences of graphs has proven to be difficult. In this work, we take a step in this direction by proposing two models for graph sequences that capture: (a) link persistence between nodes across time, and (b) community persistence of each node across time.