Related papers: Topological Feature Selection
We introduce a technique to filter out complex data-sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is…
Current modularity-based community detection algorithms attempt to find cluster memberships that maximize modularity within a fixed graph topology. Diverging from this conventional approach, our work introduces a novel strategy that employs…
In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other…
The traditional Triangular Maximally Filtered Graph (TMFG) construction requires pre-computation and storage of a dense correlation matrix; this limits its applicability to small and medium-sized datasets. Here we identify key memory and…
Inferring missing links or detecting spurious ones based on observed graphs, known as link prediction, is a long-standing challenge in graph data analysis. With the recent advances in deep learning, graph neural networks have been used for…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
Graph neural networks have become a staple in problems addressing learning and analysis of data defined over graphs. However, several results suggest an inherent difficulty in extracting better performance by increasing the number of…
In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…
Let $N$ local decision makers in a sensor network communicate with their neighbors to reach a decision \emph{consensus}. Communication is local, among neighboring sensors only, through noiseless or noisy links. We study the design of the…
Link prediction systems (e.g. recommender systems) typically use graph topology as one of their main sources of information. However, automorphisms and related properties of graphs beget inherent limits in predictability. We calculate hard…
Social networks have become an inseparable part of human life and processing them in an efficient manner is a top priority in the study of networks. These networks are highly dynamic and they are growing incessantly. Inspired by the concept…
Semi-supervised node classification in attributed graphs, i.e., graphs with node features, involves learning to classify unlabeled nodes given a partially labeled graph. Label predictions are made by jointly modeling the node and its'…
In colored graphs, node classes are often associated with either their neighbors class or with information not incorporated in the graph associated with each node. We here propose that node classes are also associated with topological…
In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…
This paper introduces a generalization of Convolutional Neural Networks (CNNs) to graphs with irregular linkage structures, especially heterogeneous graphs with typed nodes and schemas. We propose a novel spatial convolution operation to…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
The main approaches for node classification in graphs are information propagation and the association of the class of the node with external information. State of the art methods merge these approaches through Graph Convolutional Networks.…
In machine learning and pattern recognition, feature selection has been a hot topic in the literature. Unsupervised feature selection is challenging due to the loss of labels which would supply the related information.How to define an…
Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to…