Semantic Neighborhoods as Hypergraphs

Ambiguity preserving representations such as lattices are very useful in a number of NLP tasks, including paraphrase generation, paraphrase recognition, and machine translation evaluation. Lattices compactly represent lexical variation, but word order variation leads to a combinatorial explosion of states. We advocate hypergraphs as compact representations for sets of utterances describing the same event or object. We present a method to construct hypergraphs from sets of utterances, and evaluate this method on a simple recognition task. Given a set of utterances that describe a single object or event, we construct such a hypergraph, and demonstrate that it can recognize novel descriptions of the same event with high accuracy

An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them

Structural Deep Embedding for Hyper-Networks

Network embedding has recently attracted lots of attentions in data mining. Existing network embedding methods mainly focus on networks with pairwise relationships. In real world, however, the relationships among data points could go beyond pairwise, i.e., three or more objects are involved in each relationship represented by a hyperedge, thus forming hyper-networks. These hyper-networks pose great challenges to existing network embedding methods when the hyperedges are indecomposable, that is to say, any subset of nodes in a hyperedge cannot form another hyperedge. These indecomposable hyperedges are especially common in heterogeneous networks. In this paper, we propose a novel Deep Hyper-Network Embedding (DHNE) model to embed hyper-networks with indecomposable hyperedges. More specifically, we theoretically prove that any linear similarity metric in embedding space commonly used in existing methods cannot maintain the indecomposibility property in hyper-networks, and thus propose a new deep model to realize a non-linear tuplewise similarity function while preserving both local and global proximities in the formed embedding space. We conduct extensive experiments on four different types of hyper-networks, including a GPS network, an online social network, a drug network and a semantic network. The empirical results demonstrate that our method can significantly and consistently outperform the state-of-the-art algorithms.Comment: Accepted by AAAI 1

Towards hypergraph cognitive networks as feature-rich models of knowledge

Semantic networks provide a useful tool to understand how related concepts are retrieved from memory. However, most current network approaches use pairwise links to represent memory recall patterns. Pairwise connections neglect higher-order associations, i.e. relationships between more than two concepts at a time. These higher-order interactions might covariate with (and thus contain information about) how similar concepts are along psycholinguistic dimensions like arousal, valence, familiarity, gender and others. We overcome these limits by introducing feature-rich cognitive hypergraphs as quantitative models of human memory where: (i) concepts recalled together can all engage in hyperlinks involving also more than two concepts at once (cognitive hypergraph aspect), and (ii) each concept is endowed with a vector of psycholinguistic features (feature-rich aspect). We build hypergraphs from word association data and use evaluation methods from machine learning features to predict concept concreteness. Since concepts with similar concreteness tend to cluster together in human memory, we expect to be able to leverage this structure. Using word association data from the Small World of Words dataset, we compared a pairwise network and a hypergraph with N=3586 concepts/nodes. Interpretable artificial intelligence models trained on (1) psycholinguistic features only, (2) pairwise-based feature aggregations, and on (3) hypergraph-based aggregations show significant differences between pairwise and hypergraph links. Specifically, our results show that higher-order and feature-rich hypergraph models contain richer information than pairwise networks leading to improved prediction of word concreteness. The relation with previous studies about conceptual clustering and compartmentalisation in associative knowledge and human memory are discussed

Attributed Stream Hypergraphs: temporal modeling of node-attributed high-order interactions

Recent advances in network science have resulted in two distinct research directions aimed at augmenting and enhancing representations for complex networks. The first direction, that of high-order modeling, aims to focus on connectivity between sets of nodes rather than pairs, whereas the second one, that of feature-rich augmentation, incorporates into a network all those elements that are driven by information which is external to the structure, like node properties or the flow of time. This paper proposes a novel toolbox, that of Attributed Stream Hypergraphs (ASHs), unifying both high-order and feature-rich elements for representing, mining, and analyzing complex networks. Applied to social network analysis, ASHs can characterize complex social phenomena along topological, dynamic and attributive elements. Experiments on real-world face-to-face and online social media interactions highlight that ASHs can easily allow for the analyses, among others, of high-order groups' homophily, nodes' homophily with respect to the hyperedges in which nodes participate, and time-respecting paths between hyperedges.Comment: Submitted to "Applied Network Science

Architectures of Topological Deep Learning: A Survey on Topological Neural Networks

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a comprehensive framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. TDL has demonstrated theoretical and practical advantages that hold the promise of breaking ground in the applied sciences and beyond. However, the rapid growth of the TDL literature has also led to a lack of unification in notation and language across Topological Neural Network (TNN) architectures. This presents a real obstacle for building upon existing works and for deploying TNNs to new real-world problems. To address this issue, we provide an accessible introduction to TDL, and compare the recently published TNNs using a unified mathematical and graphical notation. Through an intuitive and critical review of the emerging field of TDL, we extract valuable insights into current challenges and exciting opportunities for future development