Higher-order Structural Features Research Articles

MGATs: Motif-Based Graph Attention Networks

In recent years, graph convolutional neural networks (GCNs) have become a popular research topic due to their outstanding performance in various complex network data mining tasks. However, current research on graph neural networks lacks understanding of the high-order structural features of networks, focusing mostly on node features and first-order neighbor features. This article proposes two new models, MGAT and MGATv2, by introducing high-order structure motifs that frequently appear in networks and combining them with graph attention mechanisms. By introducing a mixed information matrix based on motifs, the generation process of graph attention coefficients is improved, allowing the model to capture higher-order structural features. Compared with the latest research on various graph neural networks, both MGAT and MGATv2 achieve good results in node classification tasks. Furthermore, through various experimental studies on real datasets, we demonstrate that the introduction of network structural motifs can effectively enhance the expressive power of graph neural networks, indicating that both high-order structural features and attribute features are important components of network feature learning.

A Link Prediction Algorithm Based on GAN

Link prediction, as an important research direction in complicated network analysis, has broad application prospects. However, traditional link prediction algorithms are generally designed by the sparse expression of the adjacency matrix, which is computationally expensive and inefficient, being also unable to run on large-scale networks and to preserve their higher order structural features. To fill this gap, we propose a GAN (generative adversarial network)-based link prediction algorithm. The algorithm layers the network graph, preserving the local features and higher-level structural features of the original network graph, and uses a generative adversarial model to recursively and backwardly obtain the low-dimensional vector form of the vertices in each layer of the network graph as the initialization of the network graph in the previous layer. It then obtains the low-dimensional vector form of all the vertices in the original network graph for link prediction, and the problem of local minima that can be generated by random initialization is solved. The experimental results show that our method is superior to many state-of-the-art algorithms.

Important nodes mining based on a novel personalized temporal motif pagerank algorithm in temporal networks

In temporal networks, PageRank-based methods are usually used to calculate the importance of nodes. However, almost all the methods focus on the first-order relationships between nodes while ignore higher-order interactions between nodes in the graph. Considering that temporal motifs are recurring, higher-order and significant network connectivity patterns, which can capture both temporal and higher-order structural features in dynamic networks, this paper proposes a novel Personalized Temporal Motif PageRank (PTMP) algorithm to measure the importance of nodes in temporal networks. Specifically, to capture temporal information and higher-order features, we develop a method extracting temporal motif instances from temporal networks, and design an algorithm to compute the weighted motif adjacency matrix and the diagonal motif out-degree matrix, then define a motif transition matrix, which contains the personalized feature and can be used to compute the importance score of nodes. Finally, we make the steady-state analysis for the PTMP algorithm and compare it with other state-of-the-art baselines on multiple real-world datasets. The experimental results demonstrate that the PTMP algorithm is capable of mining much richer important nodes information accurately and effectively.

Role-based network embedding via structural features reconstruction with degree-regularized constraint

Role-based network embedding aims to map network into low-dimensional node representations while preserving structural similarities. Adjacency matrix contain both the local and global information of a network, but it cannot directly represent the role of nodes. So it is essential to extract higher-order structural features from adjacency matrix for role-based network embedding (structural equivalence). While being sensitive to noise in real networks in general, the features extracted by some identical methods cannot truly represent the role of nodes. Therefore, we propose a deep learning framework RESD. In detail, we first propose extracting higher-order structural features for each node in the network. Then, we utilize the Variational Auto-Encoder (VAE) to model the nonlinear relationship of the features, reduce noise and improve the robustness of embedding. Furthermore, in the embedding space, we apply a degree-regularized constraint to guide the representation learning for preserving key structural information of nodes (e.g., degrees), which may be lost due to the principle of VAE framework. Finally, we construct a unified objective function to learn the node embedding for role discovery by preserving the structural features and node degree. We compare our model with several state-of-the-art methods on real-world networks. The results of extensive experiments demonstrate the effectiveness of our model and prove that our model scales well with dimension and network size.

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.

Graph Embedding via Graph Summarization

Graph representation learning aims to represent the structural and semantic information of graph objects as dense real value vectors in low dimensional space by machine learning. It is widely used in node classification, link prediction, and recommendation systems. However, directly computing the embeddings for original graphs is prohibitively inefficient, especially for large-scale graphs. To address this issue, we present the GSE (Graph Summarization Embedding) model, a more efficient model that computes the nodes’ embeddings based on graph summarization. Specifically, the model first searches for the minimum information entropy of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> groups to transform the original graph into a hypergraph with higher-order structural features. Next, the summarization graph’s connection probabilities are used to determine the biased random walks on the hypergraph, which then generates the sequences of the super-nodes. Finally, the node sequences are fed into the skip-gram to generate the vectors of these nodes. Our proposed model improves the efficiency of graph embedding on big data graphs and effectively alleviates the local optimal problem caused by the random walks. Experimental results demonstrate that GSE outperforms main existing clustering baselines, such as K_Means Clustering, Affinity Propagation Clustering, Canopy Clustering, and ACP Clustering. Moreover, our model can be coupled with the main graph embedding methods and improves the Macro-F1 scores and Micro-F1 scores for classification tasks on a variety of real-world graph data.

Single document keyword extraction via quantifying higher-order structural features of word co-occurrence graph

Keyword extraction is a building block of information retrieval. Many techniques have been developed to tackle this problem. However, most of the existing methods suffer from high computational complexity or large corpus dependency, which limits the practical applications. Indeed, given a single document, new visions and strategies are needed for keyword extraction to face the challenges. In this work, we proposed a new graph-based measure for keyword extraction, by leveraging higher-order structural features (e.g. motifs) of word co-occurrence graph. The experiments on real datasets shows superior performance of the proposed method, compared to TF-IDF and PageRank based methods.

Structural Representation Learning for User Alignment Across Social Networks

Aligning users across different social networks has become increasingly studied as an important task to social network analysis. In this paper, we propose a novel representation learning method that mainly exploits social structures for the network alignment. In particular, the proposed network embedding framework models the follower-ship and followee-ship of each user explicitly as input and output context vectors, while preserving the proximity of users with “similar” followers and followees in the embedded space. We incorporate both known and predicted user anchors across the networks as constraints to facilitate the transfer of context information to achieve accurate user alignment. Both network embedding and user alignment are inferred under a unified optimization framework with negative sampling adopted to ensure scalability. Also, variants of the proposed framework, including the incorporation of higher-order structural features, are also explored for further boosting the alignment accuracy. Extensive experiments on large-scale social and academia network datasets demonstrate the efficacy of our proposed model compared with state-of-the-art methods.

HARP: Hierarchical Representation Learning for Networks

We present HARP, a novel method for learning low dimensional embeddings of a graph’s nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively avoiding troublesome embedding configurations (i.e. local minima) which can pose problems to non-convex optimization. HARP works by finding a smaller graph which approximates the global structure of its input. This simplified graph is used to learn a set of initial representations, which serve as good initializations for learning representations in the original, detailed graph. We inductively extend this idea, by decomposing a graph in a series of levels, and then embed the hierarchy of graphs from the coarsest one to the original graph. HARP is a general meta-strategy to improve all of the state-of-the-art neural algorithms for embedding graphs, including DeepWalk, LINE, and Node2vec. Indeed, we demonstrate that applying HARP’s hierarchical paradigm yields improved implementations for all three of these methods, as evaluated on classification tasks on real-world graphs such as DBLP, BlogCatalog, and CiteSeer, where we achieve a performance gain over the original implementations by up to 14% Macro F1.

Comparative study of cellulosic components isolated from different Eucalyptus species

Seven selected Eucalyptus varieties grown under the same conditions were collected to investigate the relationships between specie type and cellulose composition as well as structural and thermo-chemical properties. This systematic investigation used E. badjensis, E. benthamii, E. dunnii, E. globulus, E. nitens, E. smithii and two hybrids, E. nitens × E. globulus, from which holocellulose and alpha-cellulose were isolated. The results indicated no significant correlation between the molecular fingerprints and higher order structural features (crystallinity via X-ray diffraction, CrI XRD). Compared to the cellulosic source, the same techniques revealed higher CrI for the isolated holocellulose. The opposite applied to the CrI of alpha-cellulose. CrI spanned the range between 39 and 55%, and crystallite sizes spanned 1.8–4.4 nm range. The cellulose from the Eucalyptus samples displayed distinctive chemical fingerprints and thermal degradation (thermogravimetric analysis, TGA), the latter of which occurred in a wide range of temperature, between 338 and 369 °C. Most remarkably, a significant correlation was observed between CrI XRD and TGA from the wood samples. Moreover, the thermal degradation of alpha-cellulose correlated strongly with the crystallite size. In wood and holocellulose samples, E. badjensis and E. smithii showed the lowest CrI and thermal degradation of cellulose, while En × Eg hybrids showed the highest values. Alpha-cellulose from E. dunni underwent the highest thermal degradation and E. smithii displayed the highest CrI. Such differences are expected to be relevant to the processing and quality of cellulose derivatives, a subject that is yet to be evaluated.

Atomic-scale characterization of conformational changes in the preQ 1 riboswitch aptamer upon ligand binding

Riboswitches are mRNA structural elements that act as intracellular sensors of small-molecule metabolites. By undergoing conformational changes capable of modulating translation or terminating transcription, riboswitches are able to play a role in regulating the concentration of essential metabolites in the cell. Computer-guided fluorescence experiments were carried out to interrogate molecular dynamics and conformational changes in the minimal riboswitch aptamer that binds 7-aminomethyl-7-deazaguanine (preQ 1). Our combined experimental results and computational analysis suggest that the preQ 1 riboswitch apo form is structured but shows no evidence of a ligand-binding pocket. Simulations of the apo and bound forms indicate a large conformational change is triggered by the breaking of the Watson–Crick base pairing of nucleotides G11 and C31 upon preQ 1 removal, followed by collapse of the pocket due to interfering π-stacking. Computational predictions of local aptamer dynamics were validated by fluorescence experiments employing 2-aminopurine substitutions. In-line probing reactions confirmed that fluorophore-labeled riboswitches retain similar higher-order structural features as the unlabeled aptamer upon ligand binding, although their affinity for the ligand is reduced by the introduction of the fluorescent reporter.

Triplet Analysis That Identifies Unpaired Regions of Functional RNAs

We developed a novel method for analyzing RNA sequences, deemed triplet analysis, and applied the method in an in vitro RNA selection experiment in which HIV-1 Tat was the target. Aptamers are nucleic acids that bind a desired target (bait), and to date, many aptamers have been identified by in vitro selection from enough concentrated libraries in which many RNAs had an obvious consensus primary sequence after sufficient cycles of the selection. Therefore, the higher-order structural features of the aptamers that are indispensable for interaction with the bait must be determined by additional investigation of the aptamers. In contrast, our triplet analysis enabled us to extract important information on functional primary and secondary structure from minimally concentrated RNA libraries. As a result, by using our method, an important unpaired region that is similar to the bulge of TAR was readily predicted from a partially concentrated library in which no consensus sequence was revealed by a conventional sequence analysis. Moreover, our analysis method may be used to assess a variety of structural motifs with desired function.

P2-067: PIB binding in Alzheimer's disease and nonhuman primate brain

Background: The amyloid cascade hypothesis implicates the Abeta peptide as an upstream effector in Alzheimer’s disease (AD) neurodegeneration. However, the deposition of Abeta in the human brain is not always associated with frank dementia, inasmuch as abundant Abeta lesions are sometimes found in the brains of aged humans without overt cognitive impairment. Furthermore, age-related accumulation of cerebral Abeta is commonly observed in nonhuman primates, yet no nonhuman species has been shown to exhibit the full behavioral or pathological characteristics of AD. Because of their close biological relationship to humans, nonhuman primates are a unique model of nonpathologic Abeta accumulation. We have extensively characterized cerebral Abeta populations in AD, aged chimpanzees, rhesus macaques, and squirrel monkeys. Methods: Using immunohistochemistry, ELISA, immunoprecipitation/ MALDI-TOF MS and in vivo Abeta-seeding assays, we found that Abeta populations are quantitatively and qualitatively similar in AD and nonhuman primate brain. To explain the pathological differences between humans and other primates, we hypothesized that higher-order structural features distinguish toxic Abeta in AD brain from the relatively benign Abeta in nonhuman primates. Recent reports show that Pittsburgh Compound B (PIB), a radioligand used for in vivo PET imaging of amyloid, binds with high affinity and stoichiometry to AD brain but with low stoichiometry to synthetic Abeta and to the Abeta deposits in transgenic mouse brain. We measured the binding of 3H-PIB to cortical homogenates from AD and nonhuman primate cases, all of which had been characterized for total soluble and insoluble Abeta levels. Results: We found that 3H-PIB binds with low stoichiometry to Abeta in nonhuman primate cortical homogenates, even in cases with levels of Abeta equal to those in AD. Conclusions: These data suggest that cerebral beta-amyloid deposits in aged nonhuman primates, which naturally develop cerebral beta-amyloidosis over the course of many years, are structurally distinct from those in humans with AD, and that high-affinity PIB binding may be relatively selective for pathogenic Abeta in the AD brain.

Controlling amyloid growth in multiple dimensions

The great progress made in defining the structure of protein and peptide amyloid assemblies, particularly the arrangement of peptides in β-sheets, is counterbalanced by the still poor understanding of the higher organization of β-sheets within the fibril and overall fibril/fibril associations. The assembly pathway and basis of amyloid toxicity may well depend on these higher-order structural features. For example, significant evidence points to association between sheets as the rate limiting step in fibril assembly, and a critical metal binding site has now been identified that involves residues from different individual sheets. Here we review experiments that are identifying some of the issues associated with sheet–sheet association by investigating simple model peptides derived from the central core of the Aβ peptide implicated in Alzheimer's disease. These peptides transit between fibril/ribbon/nanotube morphologies in response to assembly conditions, laying the foundation for understanding the folding landscape for these higher order assemblies, revealing potential targets for therapeutic intervention, and opening strategies for the design of highly ordered peptide self-assembled microscale morphologies.

Characterization of leucine zipper complexes by electrospray ionization mass spectrometry.

The development of "soft" ionization methods has enabled the mass spectrometric analysis of higher-order structural features of proteins. We have applied electrospray ionization mass spectrometry (ESI-MS) to the analysis of the number and composition of polypeptide chains in homomeric and heteromeric leucine zippers. In comparison with other methods that have been used to analyze leucine zippers, such as analytical ultracentrifugation, gel chromatography, or electrophoretic band shift assays, ESI-MS is very fast and highly sensitive and provides a straightforward way to distinguish between homomeric and heteromeric coiled-coil structures. ESI-MS analyses were carried out on the parallel dimeric leucine zipper domain GCN4-p1 of the yeast transcription factor GCN4 and on three synthetic peptides with the sequences Ac-EYEALEKKLAAX1EAKX2QALEKKLEALEHG-amide: peptide LZ (X1, X2 = Leu), peptide LZ(12A) (X1 = Ala, X2 = Leu), and peptide LZ(16N) (X1 = Leu, X2 = Asn). Equilibrium ultracentrifugation analysis showed that LZ forms a trimeric coiled coil and this could be confirmed unequivocally by ESI-MS as could the dimeric nature of GCN4-p1. The formation of heteromeric two- and three-stranded leucine zippers composed of chains from LZ and LZ(12A), or from GCN4-p1 and LZ, was demonstrated by ESI-MS and confirmed by fluorescence quenching experiments on fluorescein-labeled peptides. The results illustrate the adaptability and flexibility of the leucine zipper motif, properties that could be useful to the design of specific protein assemblies by way of coiled-coil domains.

A Definition of the Domains Archaea, Bacteria and Eucarya in Terms of Small Subunit Ribosomal RNA Characteristics

The number of small subunit rRNA sequences is now great enough that the three domains Archaea, Bacteria and Eucarya (Woese et al., 1990) can be reliably defined in terms of their sequence "signatures". Approximately 50 homologous positions (or nucleotide pairs) in the small subunit rRNA characterize and distinguish among the three. In addition, the three can be recognized by a variety of nonhomologous rRNA characters, either individual positions and/or higher-order structural features. The Crenarchaeota and the Euryarchaeota, the two archaeal kingdoms, can also be defined and distinguished by their characteristic compositions at approximately fifteen positions in the small subunit rRNA molecule.

Specificity determinants for tyrosine protein kinases

Hirudin, the powerful anticoagulant agent of leech (Hirudo medicinalis) saliva, was readily phosphorylated by two spleen tyrosine protein kinases (TPK-IIB and TPK-III) at Tyr63 with Km values of 238 microM and 74 microM, respectively. The synthetic tridecapeptide DGDFEEIPEEYLQ, corresponding to the hirudin 53-65 C-terminal fragment, was phosphorylated even more efficiently than hirudin itself. Four hirudin mutants, in which one or more of the glutamic acids at positions 57, 58, 61 and 62 have been replaced by glutamines, were poorer substrates than hirudin. The mutant in which all four glutamates were substituted, [Gln57,58,61,62]hirudin, was virtually not phosphorylated by either TPK-IIB and TPK-III. Substitution of Glu57 and Glu58 was less deleterious than substitution of the two glutamic acids adjacent to Tyr63: [Gln61,62]hirudin exhibited a 20-fold lower phosphorylation efficiency with TPK-IIB. With TPK-III, however, the Km value of [Gln61,62]hirudin was slightly lower, while the Vmax decreased sixfold. The substitution of Glu62 alone was also more detrimental with TPK-IIB than with TPK-III. The behaviour of a third spleen TPK, named lyn TPK-I and belonging to the src family, was markedly different in that it did not phosphorylate hirudin but exhibited significant activity towards [Gln57,58,61,62]hirudin. Taken together, these data confirm and extend with a protein substrate the results obtained with short model peptides which indicated the stringent substrate requirements of TPK-IIB (and of TPK-III to a lesser extent) for N-terminal acidic residues. In contrast, such residues are deleterious with lyn TPK-I. These observations also support the concept that tyrosine protein kinases recognize specificity determinants situated in the vicinity of the target residue rather than requiring higher-order structural features.

Pattern searching/alignment with RNA primary and secondary structures: an effective descriptor for tRNA

A convenient pattern-matching program using primary and higher-order structural features has been developed based on a 'backtracking' algorithm. A second implementation of the algorithm uses descriptors of structural features (including primary sequences) to align a list of homologous or highly similar sequences. An application of the pattern matcher to the search for tRNA and group I intron structural motifs in sequence data banks is presented. The design of a highly discriminate tRNA motif, common to all cellular tRNAs and not found in a control sequence bank, was accomplished using the pattern matcher in conjunction with the alignment program.

Structure detection through automated covariance search

This paper summarizes our investigations into the computational detection of secondary and tertiary structure of ribosomal RNA. We have developed a new automated procedure that not only identifies potential secondary and tertiary structural interactions, but also provides the covariation evidence that supports the proposed bondings, and any counterevidence that can be detected in the known sequences. A small number of previously unknown higher-order structural features have been detected in individual RNA molecules (16S rRNA and 7S RNA) through the use of our automated procedure. We are systematically studying mitochondrial rRNA, seeking tertiary structure within 16S rRNA and quaternary structure between 16S and 23S rRNA. To test hypotheses suggested by an examination of our program's output, our colleagues in biology are sequencing key portions of the 23S ribosomal RNA for species in which the known 16S ribosomal RNA exhibits variation (from the dominant pattern) at the site of a proposed bonding. Our ultimate hope is that automated covariation analysis will contribute significantly to a refined picture of ribosomal structure.