Higher-order Structural Information Research Articles

Auto-weighted Tensor Schatten p-Norm for Robust Multi-view Graph Clustering

Recently, tensor-singular value decomposition based tensor-nuclear norm (t-TNN) has achieved impressive performance for multi-view graph clustering. This primarily ascribes the superiority of t-TNN in exploring high-order structure information among views. However, 1) t-TNN cannot ideally approximate to the original rank minimization, which produces the suboptimal graph tensor; in addition, t-TNN treats different singular values equally, such that the larger singular values corresponding to certain significant feature information (i.e., prior information) has not been utilized fully; 2) the data of original high-dimensional space are often corrupted by noise and outliers, which always makes adaptive neighbors graph learning (ANGL) generate low-quality affinity graphs. To address these issues, we propose a novel multi-view graph clustering method termed auto-weighted tensor Schatten p-norm (t-ATSN) for robust multi-view graph clustering (t-ATSN-RMGC). Concretely, we first propose t-SVD based t-ATSN with 0<p<1 to make the learned graph tensor better approximate the target rank than t-TNN. Meanwhile, it can also automatically and appropriately shrink singular values for constructing a more refined graph tensor, so as to fully capture spatial structure in the graph tensor. Moreover, we introduce the Geman McClure loss function to enhance the robustness of ANGL for noise and outliers. Experimental results on benchmarks across different scenarios and sizes show that the proposed method consistently outperforms state-of-the-art methods.

Recommendation of Knowledge Graph Convolutional Networks Based on Multilayer BiLSTM and Self-Attention

To solve the problems of cold start, sparse data, and poor recommendation performance in collaborative filtering recommendation, an end-to-end framework algorithm based on BiLSTM and BAGCN was proposed. In order to discover the higher-order structural information in the knowledge graph, stacked BiLSTM is used to extract the features of embedded entities and relationships, respectively, and the depth dependence features of user-item interaction matrix are mined. The neighborhood representation of each entity is then calculated by sampling adjacent entities of a fixed size. Then, the self-attention mechanism is used to learn the semantic association between entities and neighboring entities to obtain the final neighborhood information. Aggregators are used to combine neighborhood information and bias information when computing node representations. By extending the sampling of adjacent entities to multihop simulation of higher-order adjacent information, users’ potential long-distance interests can be captured. Compared with the baseline model, the superiority of this method is verified.

Hypergraph-Supervised Deep Subspace Clustering

Auto-encoder (AE)-based deep subspace clustering (DSC) methods aim to partition high-dimensional data into underlying clusters, where each cluster corresponds to a subspace. As a standard module in current AE-based DSC, the self-reconstruction cost plays an essential role in regularizing the feature learning. However, the self-reconstruction adversely affects the discriminative feature learning of AE, thereby hampering the downstream subspace clustering. To address this issue, we propose a hypergraph-supervised reconstruction to replace the self-reconstruction. Specifically, instead of enforcing the decoder in the AE to merely reconstruct samples themselves, the hypergraph-supervised reconstruction encourages reconstructing samples according to their high-order neighborhood relations. By the back-propagation training, the hypergraph-supervised reconstruction cost enables the deep AE to capture the high-order structure information among samples, facilitating the discriminative feature learning and, thus, alleviating the adverse effect of the self-reconstruction cost. Compared to current DSC methods, relying on the self-reconstruction, our method has achieved consistent performance improvement on benchmark high-dimensional datasets.

HM-Modularity: A Harmonic Motif Modularity Approach for Multi-Layer Network Community Detection

Multi-layer network community detection has drawn an increasing amount of attention recently. Despite success, the existing methods mainly focus on the lower-order connectivity structure at the level of individual nodes and edges. And the higher-order connectivity structure has been largely ignored, which contains better signature of community compared with edges. The main challenges in utilizing higher-order structure for multi-layer network community detection are that the most representative higher-order structure may vary from one layer to another and the connectivity structure formed by the same node subset may exhibit different higher-order connectivity patterns in different layers. To this end, this paper proposes a novel higher-order structure, termed harmonic motif, which is a dense subgraph having on average the largest statistical significance in each layer. Based on the harmonic motif, a primary layer is constructed by integrating higher-order structural information from all layers. Additionally, the higher-order structural information of each individual layer is taken as the auxiliary information. A coupling is established between the primary layer and each auxiliary layer. Accordingly, a harmonic motif modularity is designed to generate the community structure. Extensive experiments on eleven real-world multi-layer network datasets have been conducted to confirm the effectiveness of the proposed method.

Efficient and High-Quality Seeded Graph Matching: Employing Higher-order Structural Information

Driven by many real applications, we study the problem of seeded graph matching. Given two graphs and , and a small set of pre-matched node pairs where and , the problem is to identify a matching between and growing from , such that each pair in the matching corresponds to the same underlying entity. Recent studies on efficient and effective seeded graph matching have drawn a great deal of attention and many popular methods are largely based on exploring the similarity between local structures to identify matching pairs. While these recent techniques work provably well on random graphs, their accuracy is low over many real networks. In this work, we propose to utilize higher-order neighboring information to improve the matching accuracy and efficiency. As a result, a new framework of seeded graph matching is proposed, which employs Personalized PageRank (PPR) to quantify the matching score of each node pair. To further boost the matching accuracy, we propose a novel postponing strategy, which postpones the selection of pairs that have competitors with similar matching scores. We show that the postpone strategy indeed significantly improves the matching accuracy. To improve the scalability of matching large graphs, we also propose efficient approximation techniques based on algorithms for computing PPR heavy hitters. Our comprehensive experimental studies on large-scale real datasets demonstrate that, compared with state-of-the-art approaches, our framework not only increases the precision and recall both by a significant margin but also achieves speed-up up to more than one order of magnitude.

Meta-path Guided Heterogeneous Graph Neural Network For Dish Recommendation System

The traditional recommendation system can hardly utilize the ingredients and flavor characteristics of the dishes, and faces the problems of sparse data and cold start, resulting in inaccurate results of the recommendation system. This paper addresses these problems by constructing a heterogeneous graph network with the interaction data between users and dishes in the food domain and taking the main and auxiliary ingredients as nodes. Also, we capture the higher-order structural information among users, dishes, and main and auxiliary ingredients by using meta-path guidance. In the meantime, we assign weights to the edges associated with user nodes and main and auxiliary ingredients nodes, which can obtain users’ preferences for main and auxiliary ingredients by using weighted GCN networks. The experiments conducted on a food domain dataset demonstrate that the meta-path-guided heterogeneous graph dish recommendation algorithm proposed in this paper is improved over the traditional recommendation algorithm.

Node classification using kernel propagation in graph neural networks

In this work, we introduce a kernel propagation method that enables graph neural networks (GNNs) to leverage higher-order network structural information without increasing the complexity of the networks. Recent studies have introduced GNNs that include higher-order neighborhood features containing global network information by propagating node features using a higher-order feature propagation rule. Though these GNNs have shown to improve node classification performance, they fail to include local connectivity information. Alternatively, GNNs also concatenate increasing orders of adjacency matrix in deeper layers in order to include higher-order structural information. In addition to global network information, GNNs also make use of node features which are network and node dependent features that serve to distinguish structurally isomorphic sub-structures within graphs. However, such node features may not always be available or depending on the network, may lead to deteriorating classification performance. Hence, to resolve these limitations, we propose a kernel propagation method that introduces a pre-processing step for GNNs to leverage higher-order structural features. The higher-order structural features are computed using a weighted random walk matrix which is node independent while using the first-order spectral propagation rule which explicitly considers local connectivity. Through our benchmark experiments, we find that the computed higher-order structural features are capable of replacing node dependent features while performing node classification task with performance on par with the state of the art approaches. Further, we also find that including both node features and higher-order structural features increases the performance of GNNs on large scale benchmark networks considered in this study. Our results show that considering local and global structural information as input to GNNs lead to an improvement in node classification performance in the absence/presence of node features without loss of performance.

Social Network Embedding Method Basing Loop-free Path

Network embedding’s goal is to learn low-dimensional feature representations of nodes in a network and use the learned features in various analysis tasks of the network, such as node classification, link prediction, community discovery and recommendation. Existing network embedding methods do not make sufficient use of higher-order structural information in social networks and are not ideal for application in social networks. A Loop-free Path Combined with Attributes Network Embedding (LFNE) method is proposed to solve these problems. The algorithm first calculates the node higher-order structure similarity based on the loop-free paths between nodes, eliminates the influence of loop paths and large degree nodes on node structure similarity, and enables the network embedding method to better fuse the higher-order structure information of social networks. The node structural similarity is finally applied to the low-dimensional feature representation of the learned nodes in the stacked denoising autoencoder. Experimental comparisons with representative algorithms in recent years on three social network datasets show that the LFNE algorithm can achieve relatively significant results in node classification and link prediction experiments, with better network embedding performance.

Multikernel Clustering via Non-Negative Matrix Factorization Tailored Graph Tensor Over Distributed Networks

Next-generation wireless networks are witnessing an increasing number of clustering applications, and produce a large amount of non-linear and unlabeled data. In some degree, single kernel methods face the challenging problem of kernel choice. To overcome this problem for non-linear data clustering, multiple kernel graph-based clustering (MKGC) has attracted intense attention in recent years. However, existing MKGC methods suffer from two common problems: (1) they mainly aim to learn a consensus kernel from multiple candidate kernels, slight affinity graph learning, such that cannot fully exploit the underlying graph structure of non-linear data; (2) they disregard the high-order correlations between all base kernels, which cannot fully capture the consistent and complementary information of all kernels. In this paper, we propose a novel non-negative matrix factorization (NMF) tailored graph tensor MKGC method for non-linear data clustering, namely TMKGC. Specifically, TMKGC integrates NMF and graph learning together in kernel space so as to learn multiple candidate affinity graphs. Afterwards, the high-order structure information of all candidate graphs is captured in a 3-order tensor kernel space by introducing tensor singular value decomposition based tensor nuclear norm, such that an optimal affinity graph can be obtained subsequently. Based on the alternating direction method of multipliers, the effective local and distributed solvers are elaborated to solve the proposed objective function. Extensive experiments have demonstrated the superiority of TMKGC compared to the state-of-the-art MKGC methods.

CANE: community-aware network embedding via adversarial training

Network embedding aims to learn a low-dimensional representation vector for each node while preserving the inherent structural properties of the network, which could benefit various downstream mining tasks such as link prediction and node classification. Most existing works can be considered as generative models that approximate the underlying node connectivity distribution in the network, or as discriminate models that predict edge existence under a specific discriminative task. Although several recent works try to unify the two types of models with adversarial learning to improve the performance, they only consider the local pairwise connectivity between nodes. Higher-order structural information such as communities, which essentially reflects the global topology structure of the network, is largely ignored. To this end, we propose a novel framework called CANE to simultaneously learn the node representations and identify the network communities. The two tasks are integrated and mutually reinforce each other under a novel adversarial learning framework. Specifically, with the detected communities, CANE jointly minimizes the pairwise connectivity loss and the community assignment error to improve node representation learning. In turn, the learned node representations provide high-quality features to facilitate community detection. Experimental results on multiple real datasets demonstrate that CANE achieves substantial performance gains over state-of-the-art baselines in various applications including link prediction, node classification, recommendation, network visualization, and community detection.

High-Resolution Optical Remote Sensing Image Registration via Reweighted Random Walk Based Hyper-Graph Matching

High-resolution optical remote sensing image registration is still a challenging task due to non-linearity in the intensity differences and geometric distortion. In this paper, an efficient method utilizing a hyper-graph matching algorithm is proposed, which can simultaneously use the high-order structure information and radiometric information, to obtain thousands of feature point pairs for accurate image registration. The method mainly consists of the following steps: firstly, initial matching by Uniform Robust Scale-Invariant Feature Transform (UR-SIFT) is carried out in the highest pyramid image level to derive the approximate geometric relationship between the images; secondly, two-stage point matching is performed to find the matches, that is, a rotation and scale invariant area-based matching method is used to derive matching candidates for each feature point and an efficient hyper-graph matching algorithm is applied to find the best match for each feature point; thirdly, a local quadratic polynomial constraint framework is used to eliminate match outliers; finally, the above process is iterated until finishing the matching in the original image. Then, the obtained correspondences are used to perform the image registration. The effectiveness of the proposed method is tested with six pairs of high-resolution optical images, covering different landscape types—such as mountain area, urban, suburb, and flat land—and registration accuracy of sub-pixel level is obtained. The experiments show that the proposed method outperforms the conventional matching algorithms such as SURF, AKAZE, ORB, BRISK, and FAST in terms of total number of correct matches and matching precision.

Graph neural news recommendation with long-term and short-term interest modeling

With the information explosion of news articles, personalized news recommendation has become important for users to quickly find news that they are interested in. Existing methods on news recommendation mainly include collaborative filtering methods which rely on direct user-item interactions and content based methods which characterize the content of user reading history. Although these methods have achieved good performances, they still suffer from data sparse problem, since most of them fail to extensively exploit high-order structure information (similar users tend to read similar news articles) in news recommendation systems. In this paper, we propose to build a heterogeneous graph to explicitly model the interactions among users, news and latent topics. The incorporated topic information would help indicate a user’s interest and alleviate the sparsity of user-item interactions. Then we take advantage of graph neural networks to learn user and news representations that encode high-order structure information by propagating embeddings over the graph. The learned user embeddings with complete historic user clicks capture the users’ long-term interests. We also consider a user’s short-term interest using the recent reading history with an attention based LSTM model. Experimental results on real-world datasets show that our proposed model significantly outperforms state-of-the-art methods on news recommendation.

The Impact of Immunoglobulin G1 Fc Sialylation on Backbone Amide H/D Exchange.

The usefulness of higher-order structural information provided by hydrogen/deuterium exchange-mass spectrometry (H/DX-MS) for the structural impact analyses of chemical and post-translational antibody modifications has been demonstrated in various studies. However, the structure–function assessment for protein drugs in biopharmaceutical research and development is often impeded by the relatively low-abundance (below 5%) of critical quality attributes or by overlapping effects of modifications, such as glycosylation, with chemical amino acid modifications; e.g., oxidation or deamidation. We present results demonstrating the applicability of the H/DX-MS technique to monitor conformational changes of specific Fc glycosylation variants produced by in vitro glyco-engineering technology. A trend towards less H/DX in Fc Cγ2 domain segments correlating with larger glycan structures could be confirmed. Furthermore, significant deuterium uptake differences and corresponding binding properties to Fc receptors (as monitored by SPR) between α-2,3- and α-2,6-sialylated Fc glycosylation variants were verified at sensitive levels.

A Structure-Enriched Neural Network for network embedding

Recent years have witnessed the importance of network embedding in many fields, as well as increased attention in academia. Although a number of algorithms have been proposed in this area, most existing models which only utilize the structure topology information of networks often suffer performance losses because of their insufficiency with regard to selecting structure similar patterns, handling noise data, and/or capturing non-linear or high-order structure information. To address these challenges, in this paper, we present a novel Structure-Enriched Neural Network (SENN) for network embedding. Specifically, SENN can not only capture the complex structure similar patterns observed in networks by introducing direction adjustment parameters of the transition probability, but also introduce a stacked denoise autoencoder to perform the dimension reduction for each order matrix independently. Therefore, SENN can preserve more useful structure information and make the embeddings more robust. Moreover, SENN can effectively integrate the multi-order structure information by the combining layer with attention mechanism. Finally, to compare with other state-of-the-art methods, we conduct extensive experiments with both synthetic and real-world datasets on various tasks (e.g.,node classification, visualization). The experimental results clearly demonstrate the effectiveness of our proposed model for network embedding.

An integrated native mass spectrometry and top-down proteomics method that connects sequence to structure and function of macromolecular complexes.

Mass spectrometry (MS) has become a crucial technique for the analysis of protein complexes. Native MS has traditionally examined protein subunit arrangements, while proteomics MS has focused on sequence identification. These two techniques are usually performed separately without harvesting the synergies between them. Here we describe the development of an integrated native MS and top-down proteomics method using Fourier transform ion cyclotron resonance (FTICR) to analyze macromolecular protein complexes in a single experiment. We address previous concerns of employing FTICR MS to measure large macromolecular complexes by demonstrating the detection of complexes up to 1.8 MDa, and we demonstrate the efficacy of this technique for direct acquirement of sequence to higher order structural information with several large complexes. We then summarize the unique functionalities of different activation/dissociation techniques. The platform expands the ability of MS to integrate proteomics and structural biology to provide insights into protein structure, function and regulation.

Electron transfer dissociation provides higher-order structural information of native and partially unfolded protein complexes.

Top-down sequencing approaches are becoming ever more popular for protein characterization, due to the ability to distinguish and characterize different protein isoforms. Under non-denaturing conditions, electron transfer dissociation (ETD) can furthermore provide important information on the exposed surface of proteins or complexes, thereby contributing to the characterization of their higher-order structure. Here, we investigate this approach using top-down ETD of tetrameric hemoglobin, concanavalin A, and alcohol dehydrogenase combined with ion mobility (IM) on a commercially available quadrupole/ion mobility/time-of-flight instrument (Waters Synapt G2). By applying supplemental activation in the transfer cell (post-IM), we release ETD fragments and attain good sequence coverage in the exposed terminal regions of the protein. We investigate the correlation between observed sites of fragmentation with regions of solvent accessibility, as derived from the crystal structure. Ion acceleration prior to ETD is also used to cause collision-induced unfolding (CIU) of the complexes without monomer ejection, as evidenced by the IM profiles. These partially unfolded tetramers show efficient fragmentation in some regions which are not sequenced under more gentle MS conditions. We show that by increasing CIU in small increments and monitoring the changes in the fragmentation pattern, it is possible to follow the initial steps of gas-phase protein unfolding. Fragments from partially unfolded protein complexes are released immediately after electron transfer, prior to IM (they do not share the drift time of their precursor), and observed without the need for supplemental activation. This is further evidence that the higher-order structure in these protein regions has been disrupted.

Nonlocal denoising using anisotropic structure tensor for 3D MRI

Noise in magnetic resonance imaging (MRI) data is widely recognized to be harmful to image processing and subsequent quantitative analysis. To ameliorate the effects of image noise, the authors present a structure-tensor based nonlocal mean (NLM) denoising technique that can effectively reduce noise in MRI data and improve tissue characterization. The proposed 3D NLM algorithm uses a structure tensor to characterize information around tissue boundaries. The similarity weight of a pixel (or patch), which determines its contribution to the denoising process, is determined by the intensity and structure tensor simultaneously. Meanwhile, similarity of structure tensors is computed using an affine-invariant Riemannian metrics, which compares tensor properties more comprehensively and avoids orientation inaccuracy of structure subsequently. The proposed method is further extended for denoising high dimensional MRI data such as diffusion weighted MRI. It is also extended to handle Rician noise corruption so that denoising effects are further enhanced. The proposed method was implemented in both simulated datasets and multiply modalities of real 3D MRI datasets. Comparisons with related state-of-the-art algorithms demonstrated that this method improves denoising performance qualitatively and quantitatively. In this paper, high order structure information of 3D MRI was characterized by 3D structure tensor and compared for NLM denoising in a Riemannian space. Experiments with simulated and real human MRI data demonstrate a great potential of the proposed technique for routine clinical use.

A superior descriptor of random textures and its predictive capacity

Two-phase random textures abound in a host of contexts, including porous and composite media, ecological structures, biological media, and astrophysical structures. Questions surrounding the spatial structure of such textures continue to pose many theoretical challenges. For example, can two-point correlation functions be identified that can be manageably measured and yet reflect nontrivial higher-order structural information about the textures? We present a solution to this question by probing the information content of the widest class of different types of two-point functions examined to date using inverse "reconstruction" techniques. This enables us to show that a superior descriptor is the two-point cluster function C(2)(r), which is sensitive to topological connectedness information. We demonstrate the utility of C(2)(r) by accurately reconstructing textures drawn from materials science, cosmology, and granular media, among other examples. Our work suggests a theoretical pathway to predict the bulk physical properties of random textures and that also has important ramifications for atomic and molecular systems.

Toward the Three-Dimensional Structure of the Escherichia coli DNA-Binding Protein H-NS: A CD and Fluorescence Study

The DNA-binding protein H-NS compacts DNA and acts as a specific transcription factor regulating the expression of various bacterial genes. The small abundant protein binds to curved DNA without apparent sequence specificity and the exact nature of its DNA interaction is still unknown. H-NS lacks any common DNA-binding or oligomerization motif and except for a C-terminal fragment of the protein no high resolution structural information is available today. Since the complete structure of H-NS is of considerable interest for understanding its versatile regulatory features, and in lack of high-resolution data for the complete molecule, we have combined circular dichroism (CD) and fluorescence measurements to collect secondary- and higher-order structural information on H-NS. Comparison of CD analyses of wild type H-NS and functional defective mutants allowed assigning secondary structure elements to the N-terminal oligomerization domain of the protein. Moreover, according to fluorescence energy-transfer data we calculate a 45 Å distance between the DNA-binding and the oligomerization domain of H-NS.

Observation of hydrogen-deuterium exchange of ubiquitin by direct analysis of electrospray capillary-skimmer dissociation with Fourier transform ion cyclotron resonance mass spectrometry.

The structure of ubiquitin, a small cytoplasmic protein with an extended beta-sheet and an alpha-helix surrounding a hydrophobic core, has been characterized by hydrogen-deuterium (H/D) exchange labeling in conjunction with successive analysis by capillary-skimmer dissociation with electrospray ionization-Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICR MS). The deuterium content of each fragment ion was investigated at different times, and the results indicate that the deuterium incorporation rate into the backbone amides of ubiquitin varied depending on the environment of the amide hydrogens. Amide hydrogens of the N-terminal beta-strand showed quite slow exchange while those of the 35-39 loop were exchanged within a short exposure time to deuterium oxide. It was also possible to evaluate the difference in hydrogen-bond stability. The present data are consistent with the structural features obtained by X-Ray and NMR analyses. Although some of the labeling information might be lost by the scrambling of amide protons during capillary-skimmer dissociation, the results demonstrate that the present method provides useful higher-order structural information for proteins.