Hypergraph Model Research Articles

Link Prediction with Hypergraphs via Network Embedding

Network embedding is a promising field and is important for various network analysis tasks, such as link prediction, node classification, community detection and others. Most research studies on link prediction focus on simple networks and pay little attention to hypergraphs that provide a natural way to represent complex higher-order relationships. In this paper, we propose a link prediction method with hypergraphs using network embedding (HNE). HNE adapts a traditional network embedding method, Deepwalk, to link prediction in hypergraphs. Firstly, the hypergraph model is constructed based on heterogeneous library loan records of seven universities. With a network embedding method, the low-dimensional vectors are obtained to extract network structure features for the hypergraphs. Then, the link prediction is implemented on the hypergraphs as the classification task with machine learning. The experimental results on seven real networks show our approach has good performance for link prediction in hypergraphs. Our method will be helpful for human behavior dynamics.

Hypergraph-based importance assessment for binary classification data

We present a novel hypergraph-based framework enabling an assessment of the importance of binary classification data elements. Specifically, we apply the hypergraph model to rate data samples’ and categorical feature values’ relevance to classification labels. The proposed Hypergraph-based Importance ratings are theoretically grounded on the hypergraph cut conductance minimization concept. As a result of using hypergraph representation, which is a lossless representation from the perspective of higher-order relationships in data, our approach allows for more precise exploitation of the information on feature and sample coincidences. The solution was tested using two scenarios: undersampling for imbalanced classification data and feature selection. The experimentation results have proven the good quality of the new approach when compared with other state-of-the-art and baseline methods for both scenarios measured using the average precision evaluation metric.

Dimensionality reduction using local-global standard hypergraph embedding for rotor fault diagnosis

The vibration signal contains a lot of state information, and its time domain, frequency domain, and time-frequency domain features are extracted to describe the rotor’s operational state in detail. However, multi-domain and multi-angle feature extraction can lead to information redundancy, causing the ‘dimensionality catastrophe’ problem, which also makes fault classification more difficult. Dimensionality reduction (DR) is a technique that can help with this issue, but the majority of current DR algorithms are based on a simple intrinsic structure. To accurately characterize the intrinsic structure of high-dimensional fault dataset, this study proposed a novel DR algorithm that considers local information, global information, and the hypergraph model, named local–global standard hypergraph embedding (LGSHE). LGSHE redefines the hypergraph weight matrix’s calculation formula and constructs the local intra-class standard hypergraph, local inter-class standard hypergraph, global intra-class standard hypergraph, and global inter-class standard hypergraph to characterize the fault data structure. LGSHE can accurately characterize the intrinsic structure of high-dimensional fault dataset and increase fault classification accuracy. The performance of LGSHE is validated on two different structures of double-span rotor experimental benches, and the results show that the algorithm can achieve good fault classification accuracy.

Hypergraph geometry reflects higher-order dynamics in protein interaction networks

Protein interactions form a complex dynamic molecular system that shapes cell phenotype and function; in this regard, network analysis is a powerful tool for studying the dynamics of cellular processes. Current models of protein interaction networks are limited in that the standard graph model can only represent pairwise relationships. Higher-order interactions are well-characterized in biology, including protein complex formation and feedback or feedforward loops. These higher-order relationships are better represented by a hypergraph as a generalized network model. Here, we present an approach to analyzing dynamic gene expression data using a hypergraph model and quantify network heterogeneity via Forman-Ricci curvature. We observe, on a global level, increased network curvature in pluripotent stem cells and cancer cells. Further, we use local curvature to conduct pathway analysis in a melanoma dataset, finding increased curvature in several oncogenic pathways and decreased curvature in tumor suppressor pathways. We compare this approach to a graph-based model and a differential gene expression approach.

Scalable Graph Convolutional Network Training on Distributed-Memory Systems

Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the convolution operation on graphs induces irregular memory access patterns, designing a memory- and communication-efficient parallel algorithm for GCN training poses unique challenges. We propose a highly parallel training algorithm that scales to large processor counts. In our solution, the large adjacency and vertex-feature matrices are partitioned among processors. We exploit the vertex-partitioning of the graph to use non-blocking point-to-point communication operations between processors for better scalability. To further minimize the parallelization overheads, we introduce a sparse matrix partitioning scheme based on a hypergraph partitioning model for full-batch training. We also propose a novel stochastic hypergraph model to encode the expected communication volume in mini-batch training. We show the merits of the hypergraph model, previously unexplored for GCN training, over the standard graph partitioning model which does not accurately encode the communication costs. Experiments performed on real-world graph datasets demonstrate that the proposed algorithms achieve considerable speedups over alternative solutions. The optimizations achieved on communication costs become even more pronounced at high scalability with many processors. The performance benefits are preserved in deeper GCNs having more layers as well as on billion-scale graphs.

Preferential attachment hypergraph with high modularity

AbstractNumerous works have been proposed to generate random graphs preserving the same properties as real-life large-scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs exist, and also, just a few models allow to both preserve a power-law degree distribution and a high modularity indicating the presence of communities. We present a dynamic preferential attachment hypergraph model which features partition into communities. We prove that its degree distribution follows a power-law, and we give theoretical lower bounds for its modularity. We compare its characteristics with a real-life co-authorship network and show that our model achieves good performances. We believe that our hypergraph model will be an interesting tool that may be used in many research domains in order to reflect better real-life phenomena.

Co-Saliency Detection of RGBD Image Based on Superpixel and Hypergraph

For the co-saliency detection algorithm of an RGBD image that may have incomplete detection of common salient regions and unclear boundaries, we proposed an improved co-saliency detection method of RGBD images based on superpixels and hypergraphs. First, we optimized the depth map based on edge consistency, and introduced the optimized depth map into the SLIC algorithm to obtain the better superpixel segmentation results of RGBD images. Second, the color features, optimized depth features and global spatial features of superpixels were extracted to construct a weighted hypergraph model to generate saliency maps. Finally, we constructed a weighted hypergraph model for co-saliency detection based on the relationship of color features, global spatial features, optimized depth features and saliency features among images. In addition, in order to verify the impact of the symmetry of the optimized depth information on the co-saliency detection results, we compared the proposed method with two types of models, which included considering depth information and not considering depth information. The experimental results on Cosal150 and Coseg183 datasets showed that our improved algorithm had the advantages of suppressing the background and detecting the integrity of the common salient region, and outperformed other algorithms on the metrics of P-R curve, F-measure and MAE.

Wireless Sensor Network Coverage Optimization: Comparison of Local Search-Based Heuristics

The Maximum Lifetime Coverage Problem (MLCP) requires heuristic optimization methods due to its complexity. A real-world problem model determines how a solution is represented and the operators applied in these heuristics. Our paper describes adapting a local search scheme and its operators to MLCP optimization. The operators originate from three local search algorithms we proposed earlier: LSHMA, LSCAIA, and LSRFTA. Two steps of the LS scheme’s main loop can be executed in three different ways each. Hence, nine versions of the LS approach can be obtained. In experimental research, we verified their effectiveness. Test cases come from three benchmarks: SCP1, proposed and used in our earlier research on the three LS algorithms mentioned above, and two others found in the literature. The results obtained with SCP1 showed that the algorithm based on the hypergraph model approach (HMA) is the most effective. The remaining results of the other algorithms divide them into two groups: effective ones and weak ones. However, other benchmarks showed that the more redundant the coverage of points of interest (POIs) by sensors, the more effective the perturbation method from the approach inspired by cellular automata (CAIA). The findings expose the strengths and weaknesses of the problem-specific steps applied in the LS algorithms.

Sharp detection boundaries on testing dense subhypergraph

We study the problem of testing the existence of a dense subhypergraph. The null hypothesis corresponds to an Erdős-Rényi uniform random hypergraph and the alternative hypothesis corresponds to a uniform random hypergraph that contains a dense subhypergraph. We establish sharp detection boundaries in both scenarios: (1) the edge probabilities are known; (2) the edge probabilities are unknown. In both scenarios, sharp detection boundaries are characterized by the appropriate model parameters. Asymptotically powerful tests are provided when the model parameters fall in the detectable regions. Our results indicate that the detectable regions for general hypergraph models are dramatically different from their graph counterparts.

Learning High-Order Semantic Representation for Intent Classification and Slot Filling on Low-Resource Language via Hypergraph

Representation of language is the first and critical task for Natural Language Understanding (NLU) in a dialogue system. Pretraining, embedding model, and fine-tuning for intent classification and slot-filling are popular and well-performing approaches but are time consuming and inefficient for low-resource languages. Concretely, the out-of-vocabulary and transferring to different languages are two tough challenges for multilingual pretrained and cross-lingual transferring models. Furthermore, quality-proved parallel data are necessary for the current frameworks. Stepping over these challenges, different from the existing solutions, we propose a novel approach, the Hypergraph Transfer Encoding Network “HGTransEnNet. The proposed model leverages off-the-shelf high-quality pretrained word embedding models of resource-rich languages to learn the high-order semantic representation of low-resource languages in a transductive clustering manner of hypergraph modeling, which does not need parallel data. The experiments show that the representations learned by “HGTransEnNet” for low-resource language are more effective than the state-of-the-art language models, which are pretrained on a large-scale multilingual or monolingual corpus, in intent classification and slot-filling tasks on Indonesian and English datasets.

Disease extinction for susceptible-infected-susceptible models on dynamic graphs and hypergraphs.

We consider stochastic, individual-level susceptible-infected-susceptible models for the spread of disease, opinion, or information on dynamic graphs and hypergraphs. We set up "snapshot" models where the interactions at any time are independently and identically sampled from an underlying distribution that represents a typical scenario. In the hypergraph case, this corresponds to a new Gilbert-style random hypergraph model. After justifying this modeling regime, we present useful mean field approximations. With an emphasis on the derivation of spectral conditions that determine long-time extinction, we give computational simulations and accompanying theoretical analysis for the exact models and their mean field approximations.

DriverRWH: discovering cancer driver genes by random walk on a gene mutation hypergraph

BackgroundRecent advances in next-generation sequencing technologies have helped investigators generate massive amounts of cancer genomic data. A critical challenge in cancer genomics is identification of a few cancer driver genes whose mutations cause tumor growth. However, the majority of existing computational approaches underuse the co-occurrence mutation information of the individuals, which are deemed to be important in tumorigenesis and tumor progression, resulting in high rate of false positive.ResultsTo make full use of co-mutation information, we present a random walk algorithm referred to as DriverRWH on a weighted gene mutation hypergraph model, using somatic mutation data and molecular interaction network data to prioritize candidate driver genes. Applied to tumor samples of different cancer types from The Cancer Genome Atlas, DriverRWH shows significantly better performance than state-of-art prioritization methods in terms of the area under the curve scores and the cumulative number of known driver genes recovered in top-ranked candidate genes. Besides, DriverRWH discovers several potential drivers, which are enriched in cancer-related pathways. DriverRWH recovers approximately 50% known driver genes in the top 30 ranked candidate genes for more than half of the cancer types. In addition, DriverRWH is also highly robust to perturbations in the mutation data and gene functional network data.ConclusionDriverRWH is effective among various cancer types in prioritizes cancer driver genes and provides considerable improvement over other tools with a better balance of precision and sensitivity. It can be a useful tool for detecting potential driver genes and facilitate targeted cancer therapies.

Hypergraph Modeling via Spectral Embedding Connection: Hypergraph Cut, Weighted Kernel k-Means, and Heat Kernel

We propose a theoretical framework of multi-way similarity to model real-valued data into hypergraphs for clustering via spectral embedding. For graph cut based spectral clustering, it is common to model real-valued data into graph by modeling pairwise similarities using kernel function. This is because the kernel function has a theoretical connection to the graph cut. For problems where using multi-way similarities are more suitable than pairwise ones, it is natural to model as a hypergraph, which is generalization of a graph. However, although the hypergraph cut is well-studied, there is not yet established a hypergraph cut based framework to model multi-way similarity. In this paper, we formulate multi-way similarities by exploiting the theoretical foundation of kernel function. We show a theoretical connection between our formulation and hypergraph cut in two ways, generalizing both weighted kernel k-means and the heat kernel, by which we justify our formulation. We also provide a fast algorithm for spectral clustering. Our algorithm empirically shows better performance than existing graph and other heuristic modeling methods.

Optimization of Sparse Distributed Computations

We address the problem of the optimization of sparse matrix-vector product (SpMV) on homogeneous distributed systems. For this purpose, we propose three approaches based on partitioning the matrix into row blocks. These blocks are defined by a set of a fixed number of rows and a set of contiguous (resp. non-contiguous) rows containing a fixed number of non-zero elements. These approaches lead to solve some specific NP-hard scheduling problems. Thus, adequate heuristics are designed. We analyse the theoretical performance of the proposed approaches and validate them by a series of experiments. This work represents an important step in an overall objective which is to determine the best-balanced distribution for the SpMV computation on a distributed system. In order to validate our approaches for sparse matrix distribution, we compare them to hypergraph model as well as to PETSc library for SpMV distribution on a homogenous multicore cluster. Experimentations show that our approaches provide performances 2 times better than hypergraph and 49 times better than PETSc.

Hypergraph and Uncertain Hypergraph Representation Learning Theory and Methods

With the advent of big data and the information age, the data magnitude of various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have the ability to describe and characterize higher order relationships, which have attracted extensive attention from academia and industry in recent years. Firstly, this paper described the development process, the application areas, and the existing review research of hypergraphs; secondly, introduced the theory of hypergraphs briefly; then, compared the learning methods of ordinary graphs and hypergraphs from three aspects: matrix decomposition, random walk, and deep learning; next, introduced the structural optimization of hypergraphs from three perspectives: dynamic hypergraphs, hyperedge weight optimization, and multimodal hypergraph generation; after that, the applicability of three uncertain hypergraph models were analyzed based on three uncertainty theories: probability theory, fuzzy set, and rough set; finally, the future research directions of hypergraphs and uncertain hypergraphs were prospected.

A hypergraph-based framework for personalized recommendations via user preference and dynamics clustering

The ever-increasing number of users and items continuously imposes new challenges to existent clustering-based recommendation algorithms. To better simulate the interactions between users and items in the recommendation system, in this paper, we propose a collaborative filtering recommendation algorithm based on dynamics clustering and similarity measurement in hypergraphs (Hg-PDC). The main idea of Hg-PDC is to discover several interest communities by aggregating users with high attention, and make recommendations within each community, thereby improving the recommendation performance and reducing the time cost. Firstly, we introduce a hypergraph model to capture complex relations beyond pairwise relations, while preserving attention relations in the network. In addition, we construct a novel hypergraph model, which defines a user and his evaluated items to form a hyperedge. Secondly, an extended game dynamics clustering method is proposed for the constructed hypergraph to aggregate users with high attention into the same interest community. Here, we combine the payoff function in game theory with the traditional dynamics clustering method. Finally, we apply the dynamics clustering results and a new similarity measurement strategy with user preferences to recommend items for target users. The effectiveness of Hg-PDC is verified by experiments on six real datasets. Experimental results illustrate that our algorithm outperforms state-of-the-art algorithms in prediction errors and recommendation performance.

Dynamics of the threshold model on hypergraphs.

The threshold model has been widely adopted as a prototype for studying contagion processes on social networks. In this paper, we consider individual interactions in groups of three or more vertices and study the threshold model on hypergraphs. To understand how high-order interactions affect the breakdown of the system, we develop a theoretical framework based on generating function technology to derive the cascade condition and the giant component of vulnerable vertices, which depend on both hyperedges and hyperdegrees. First, we find a dual role of the hyperedge in propagation: when the average hyperdegree is small, increasing the size of the hyperedges may make the system fragile, while the average hyperdegree is relatively large, the increase of the hyperedges causes the system to be robust. Then, we identify the effects of threshold, hyperdegree, and hyperedge heterogeneities. The heterogeneity of individual thresholds causes the system to be more fragile, while the heterogeneity of individual hyperdegrees or hyperedges increases the robustness of the system. Finally, we show that the higher hyperdegree a vertex has, the larger possibility and faster speed it will get activated. We verify these results by simulating meme spreading on both random hypergraph models and hypergraphs constructed from empirical data.

Fuzzy Hypergraph Modeling, Analysis and Prediction of Crimes

Fuzzy Hypergraph Modeling, Analysis and Prediction of Crimes

A Self-paced Learning based Transfer Model for Hypergraph Matching

Determination of correspondences between vertexes of two graphs is one of essential tasks in the computer vision fields. Despite the graph matching problem is NP-hard, hypergraph matching is well used in many matching methods from the perspective of higher order geometric information. However, it is still a challenge to learn graph models from observed samples of graph matching. In this paper, we present an effective scheme to parameterize a graph model through self-paced learning algorithm. Consequently, each iteration heuristically selects smaller loss samples in a data-driven manner, the learning and matching problems are aligned to learn a new transfer hypergraph model for constructing its high-order structural attributes for visual object matching. For the final matching task between two graphs, we develop the transfer matching method through the assignment matrix decomposition to achieve it. Several experiments on Willow-Object datasets and some other datasets indicate the good performance of our method.

Rank-Label Anonymization for the Privacy-Preserving Publication of a Hypergraph Structure

Social networks are often published in the form of a simple graph. The simple graph representation of a social graph shows the dyadic relationship among the social entities whereas it is unable to efficiently represent the relationship among more than two entities, such as the relationship found in the social groups. This type of relationship is called super-dyadic relationship, and it can be effectively represented by a hypergraph model. This work proposes an anonymization scheme called rank-label anonymization for the privacy-preserving publication of a hypergraph structure. Here, an attack model called rank-label attack is proposed, and an anonymization solution is provided to counter this attack. The percentage of disclosure risk shows that the rank-label attack is stronger than the existing rank attack. We propose a method based on sequential clustering to achieve rank-label anonymization called sequential rank-label anonymization (SA). Another algorithm called greedy rank-label anonymization (GA) is also proposed. The quality of the anonymization solution reported by SA and GA is compared with the help of normalized anonymization cost ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NCost</i> ). Results show that the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NCost</i> reported by SA is less than that of GA for both Adult and MAG-10 datasets. In Adult dataset, approximately 58% and 62% reduction in the average execution time of GA and SA are obtained than that of a general-purpose computing system due to the use of a high-performance computing system. In MAG-10 dataset, this average reduction percentage is reported to be 56% for GA and 53% for SA. The time complexity of SA is found to be O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ) whereas it is O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) in case of GA.