Hypergraph Learning with Line Expansion

Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats vertices and hyperedges equally and proposes a new hypergraph formulation named the \emph{line expansion (LE)} for hypergraphs learning. The new expansion bijectively induces a homogeneous structure from the hypergraph by treating vertex-hyperedge pairs as "line nodes". By reducing the hypergraph to a simple graph, the proposed \emph{line expansion} makes existing graph learning algorithms compatible with the higher-order structure and has been proven as a unifying framework for various hypergraph expansions. We evaluate the proposed line expansion on five hypergraph datasets, the results show that our method beats SOTA baselines by a significant margin

Topological Deep Learning: Going Beyond Graph Data

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains. Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, we develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. We characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs in detail. Third, we evaluate the performance of CCNNs on tasks related to mesh shape analysis and graph learning. Our experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. Our findings demonstrate the advantages of incorporating higher-order relations into deep learning models in different applications

Prototype-Enhanced Hypergraph Learning for Heterogeneous Information Networks

The variety and complexity of relations in multimedia data lead to Heterogeneous Information Networks (HINs). Capturing the semantics from such networks requires approaches capable of utilizing the full richness of the HINs. Existing methods for modeling HINs employ techniques originally designed for graph neural networks, and HINs decomposition analysis, like using manually predefined metapaths. In this paper, we introduce a novel prototype-enhanced hypergraph learning approach for node classification in HINs. Using hypergraphs instead of graphs, our method captures higher-order relationships among nodes and extracts semantic information without relying on metapaths. Our method leverages the power of prototypes to improve the robustness of the hypergraph learning process and creates the potential to provide human-interpretable insights into the underlying network structure. Extensive experiments on three real-world HINs demonstrate the effectiveness of our method

DATA-DRIVEN APPROACH TO IMAGE CLASSIFICATION

Image classification has been a core topic in the computer vision community. Its recent success with convolutional neural network (CNN) algorithm has led to various real world applications such as large scale management of photos/videos on cloud/social-media, image based search for online retailers, self-driving cars, building robots and healthcare. Image classification can be broadly categorized into binary, multi-class and multi-label classification problems. Binary classification involves assigning one of the two class labels to an instance. In multi-class classification problem, an instance should be categorized into one of more than two classes. Multi-label classification is a generalized version of the multi-class classification problem where each image is assigned multiple labels as opposed to a single label. In this work, we first present various methods that take advantage of deep representations (fully connected layer of pre-trained CNN on the ImageNet dataset) and yield better performance on multi-label classification when compared to methods that use over a dozen conventional visual features. Following the success of deep representations, we intend to build a generic end-to-end deep learning framework to address all three problem categories of image classification. However, there are still no well established guidelines (in terms of choosing the number of layers to go deeper, the number of kernels and the size, the type of regularizer, the choice of non-linear function, etc.) to build an efficient deep neural network and often network architecture design is specific to a problem/dataset. Hence, we present some initial efforts in building a computational framework called Deep Decision Network (DDN) which is completely data-driven. DDN is a tree-like structured built stage-wise. During the learning phase, starting from the root network node, DDN automatically builds a network that splits the data into disjoint clusters of classes which would be handled by the subsequent expert networks. This results in a tree-like structured network driven by the data. The proposed approach provides an insight into the data by identifying the group of classes that are hard to classify and require more attention when compared to others. This feature is crucial for people trying to solve the problem with little or no domain knowledge, especially for applications in medical domain. Initially, we evaluate DDN on a binary classification problem and later extend it to more challenging multi-class and multi-label classification problems. The extension of DDN to multi-class and multi-label involves some changes but they still operate under the same underlying principle. In all the three cases, the proposed approach is tested for its recognition performance and scalability on publicly available datasets providing comparison to other methods

UniG-Encoder: A Universal Feature Encoder for Graph and Hypergraph Node Classification

Graph and hypergraph representation learning has attracted increasing attention from various research fields. Despite the decent performance and fruitful applications of Graph Neural Networks (GNNs), Hypergraph Neural Networks (HGNNs), and their well-designed variants, on some commonly used benchmark graphs and hypergraphs, they are outperformed by even a simple Multi-Layer Perceptron. This observation motivates a reexamination of the design paradigm of the current GNNs and HGNNs and poses challenges of extracting graph features effectively. In this work, a universal feature encoder for both graph and hypergraph representation learning is designed, called UniG-Encoder. The architecture starts with a forward transformation of the topological relationships of connected nodes into edge or hyperedge features via a normalized projection matrix. The resulting edge/hyperedge features, together with the original node features, are fed into a neural network. The encoded node embeddings are then derived from the reversed transformation, described by the transpose of the projection matrix, of the network's output, which can be further used for tasks such as node classification. The proposed architecture, in contrast to the traditional spectral-based and/or message passing approaches, simultaneously and comprehensively exploits the node features and graph/hypergraph topologies in an efficient and unified manner, covering both heterophilic and homophilic graphs. The designed projection matrix, encoding the graph features, is intuitive and interpretable. Extensive experiments are conducted and demonstrate the superior performance of the proposed framework on twelve representative hypergraph datasets and six real-world graph datasets, compared to the state-of-the-art methods. Our implementation is available online at https://github.com/MinhZou/UniG-Encoder

Search Behavior Prediction: A Hypergraph Perspective

Although the bipartite shopping graphs are straightforward to model search behavior, they suffer from two challenges: 1) The majority of items are sporadically searched and hence have noisy/sparse query associations, leading to a \textit{long-tail} distribution. 2) Infrequent queries are more likely to link to popular items, leading to another hurdle known as \textit{disassortative mixing}. To address these two challenges, we go beyond the bipartite graph to take a hypergraph perspective, introducing a new paradigm that leverages \underline{auxiliary} information from anonymized customer engagement sessions to assist the \underline{main task} of query-item link prediction. This auxiliary information is available at web scale in the form of search logs. We treat all items appearing in the same customer session as a single hyperedge. The hypothesis is that items in a customer session are unified by a common shopping interest. With these hyperedges, we augment the original bipartite graph into a new \textit{hypergraph}. We develop a \textit{\textbf{D}ual-\textbf{C}hannel \textbf{A}ttention-Based \textbf{H}ypergraph Neural Network} (\textbf{DCAH}), which synergizes information from two potentially noisy sources (original query-item edges and item-item hyperedges). In this way, items on the tail are better connected due to the extra hyperedges, thereby enhancing their link prediction performance. We further integrate DCAH with self-supervised graph pre-training and/or DropEdge training, both of which effectively alleviate disassortative mixing. Extensive experiments on three proprietary E-Commerce datasets show that DCAH yields significant improvements of up to \textbf{24.6\% in mean reciprocal rank (MRR)} and \textbf{48.3\% in recall} compared to GNN-based baselines. Our source code is available at \url{https://github.com/amazon-science/dual-channel-hypergraph-neural-network}.Comment: WSDM 202