High-dimensional Network Research Articles

Improved K-means Clustering Algorithm and its Applications

Background: K-means algorithm is implemented through two steps: initialization and subsequent iterations. Initialization is to select the initial cluster center, while subsequent iterations are to continuously change the cluster center until it won't change any more or the number of iterations reaches its maximum. K-means algorithm is so sensitive to the cluster center selected during initialization that the selection of a different initial cluster center will influence the algorithm performance. Therefore, improving the initialization process has become an important means of K-means performance improvement. Methods: This paper uses a new strategy to select the initial cluster center. It first calculates the minimum and maximum values of the data in a certain index (For lower-dimensional data, such as twodimensional data, features with larger variance, or the distance to the origin can be selected; for higher-dimensional data, PCA can be used to select the principal component with the largest variance), and then divides the range into equally-sized sub-ranges. Next adjust the sub-ranges based on the data distribution so that each sub-range contains as much data as possible. Finally, the mean value of the data in each sub-range is calculated and used as the initial clustering center. Results: The theoretical analysis shows that although the time complexity of the initialization process is linear, the algorithm has the characteristics of the superlinear initialization method. This algorithm is applied to two-dimensional GPS data analysis and high-dimensional network attack detection. Experimental results show that this algorithm achieves high clustering performance and clustering speed. Conclusion: This paper reduces the subsequent iterations of K-means algorithm without compromising the clustering performance, which makes it suitable for large-scale data clustering. This algorithm can not only be applied to low-dimensional data clustering, but also suitable for highdimensional data.

Symmetry-Adapted High Dimensional Neural Network Representation of Electronic Friction Tensor of Adsorbates on Metals

Nonadiabatic effects in chemical reaction at metal surfaces, due to excitation of electron-hole pairs, stand at the frontier of the studies of gas-surface reaction dynamics. However, the first principles description of electronic excitation remains challenging. In an efficient molecular dynamics with electronic friction (MDEF) method, the nonadiabatic couplings are effectively included in a so-called electronic friction tensor (EFT), which can be computed from first-order time-dependent perturbation theory (TDPT) in terms of density functional theory (DFT) orbitals. This second-rank tensor depends on adsorbate position and features a complicated transformation with regard to the intrinsic symmetry operations of the system. In this work, we develop a new symmetry-adapted neural network representation of EFT, based on our recently proposed embedded atom neural network (EANN) framework. Inspired by the derivation of the nonadiabatic coupling matrix, we represent the tensorial friction by the first and second derivatives of multiple outputs of NNs with respect to atomic Cartesian coordinates. This rigorously preserves the positive semidefiniteness, directional property, and correct symmetry-equivariance of EFT. Unlike previous methods, our new approach can readily include both molecular and surface degrees of freedom, regardless of the type of surface. Tests on the H2+Ag(111) system show that this approach yields an accurate, efficient, and continuous representation of EFT, making it possible to perform large scale TDPT-based MDEF simulations to study both adiabatic and nonadiabatic energy dissipation in a unified framework.

Two topologically different 3D CuII metal-organic frameworks assembled from the same ligands: control of reaction conditions.

Bifunctional ligands containing both carboxylic and sulfonate groups can adopt versatile coordination modes to produce novel metal-organic frameworks (MOFs) with high-dimensional networks and interesting topologies. Using 2,2'-disulfonylbiphenyl-4,4'-dicarboxylic acid (H4L) as a linker and 4,4'-bipyridine (4,4'-bpy) as a co-ligand, two novel 3D CuII MOFs, {[Cu2(L)(4,4'-bpy)2.5(H2O)]·1.7H2O}n, (1), and {[Cu2(L)(4,4'-bpy)2]·DMA·3H2O}n, (2), have been synthesized and structurally characterized by X-ray crystallography (DMA is N,N-dimethylacetamide). MOF (1) shows an unprecedented trinodal 4,4,5-connected topology network with the Schläfli symbol (4.62.73)(43.65.7.8)(6.73.8.10), while MOF (2) indicates a binodal 4,6-connected fsc network with the Schläfli symbol (44.610.8)(44.62). MOFs (1) and (2) were further characterized by elemental analysis, IR spectroscopy, powder X-ray diffraction and thermogravimetric analysis. MOF (1) shows a high water and chemical stability. The proton conductivity of (1) and CO2 adsorption of (2) were also investigated.

Monetary Policy, Industry Heterogeneity and Systemic Risk—Based on a High Dimensional Network Analysis

We utilized a high dimensional financial network to investigate the systemic risk contagion between different industries in China and to explore the impacts of monetary policy and industry heterogeneity factors. The empirical results suggest that the total level of systemic risk increased quite significantly during the 2008 global crisis and the 2015–2016 Stock Market Disaster. The energy, material, industrial, and financial sectors are the top systemic risk contributors. Industry heterogeneity variables such as the leverage ratio, book-to-market ratio, return on assets (ROA) and size have significant impacts on the systemic risk, but their effects on the systemic risk contribution are more pronounced than those on the systemic risk sensitivity. Moreover, monetary policy can effectively suppress the systemic risk diffusion derived from the leverage ratio. These results are essential for investors and regulators of risk management.

Learning epidemic threshold in complex networks by Convolutional Neural Network.

Deep learning has taken part in the competition since not long ago to learn and identify phase transitions in physical systems such as many-body quantum systems, whose underlying lattice structures are generally regular as they are in Euclidean space. Real networks have complex structural features that play a significant role in dynamics in them, and thus the structural and dynamical information of complex networks cannot be directly learned by existing neural network models. Here, we propose a novel and effective framework to learn the epidemic threshold in complex networks by combining the structural and dynamical information into the learning procedure. Considering the strong performance of learning in Euclidean space, the Convolutional Neural Network (CNN) is used, and, with the help of "confusion scheme," we can identify precisely the outbreak threshold of epidemic dynamics. To represent the high-dimensional network data set in Euclidean space for CNN, we reduce the dimensionality of a network by using graph representation learning algorithms and discretize the embedded space to convert it into an imagelike structure. We then creatively merge the nodal dynamical states with the structural embedding by multichannel images. In this manner, the proposed model can draw the conclusion from both structural and dynamical information. A large number of simulations show a great performance in both synthetic and empirical network data sets. Our end to end machine learning framework is robust and universally applicable to complex networks with arbitrary size and topology.

Dynamic relations between oil and stock market returns: A multi-country study

We study the relation between the BRENT and seventeen stock market indexes of important oil-dependent economies. We focus on connectedness between these markets and characterize the dynamics of transmission and reception. We use LASSO methods to shrink, select, and estimate the high dimensional network linking these markets between August, 1999 and March, 2018. This methodological innovation allows the inclusion of a significantly larger number of markets in the network, providing finer results regarding connectedness in the oil-stock market nexus. We show that transmission runs mainly from stock markets to the BRENT. Connectedness varies considerably over time, reaching peaks during times of financial distress. Dynamic predictive causality tests show evidence of time-varying bidirectional causality. Causality from stock markets to the BRENT is detected mostly for the last part of the sample period. This finding indicates that the impact of stock market developments on oil markets is growing over time.

SONIC: SOcial Network with Influencers and Communities

The integration of social media characteristics into an econometric framework requires modeling a high dimensional dynamic network with dimensions of parameter Θ typically much larger than the number of observations. To cope with this problem, we introduce a new structural model — SONIC which assumes that (1) a few influencers drive the network dynamics; (2) the community structure of the network is characterized as the homogeneity of response to the specific influencer, implying their underlying similarity. An estimation procedure is proposed based on a greedy algorithm and LASSO regularization. Through theoretical study and simulations, we show that the matrix parameter can be estimated even when the observed time interval is smaller than the size of the network. Using a novel dataset retrieved from a leading social media platform– StockTwits and quantifying their opinions via natural language processing, we model the opinions network dynamics among a select group of users and further detect the latent communities. With a sparsity regularization, we can identify important nodes in the network.

A Constant Factor Approximation for $d$ -Hop Connected Dominating Set in Three-Dimensional Wireless Networks

In the past few years, wireless sensor networks (WSNs) have been widely used in many areas. In these applications, sensors are remotely deployed to gather related environmental information for further analysis. To support higher scalability and better data aggregation, sensor nodes are often grouped into disjoint and mostly non-overlapping clusters. All nodes in a cluster can send their data to the cluster head within $d$ -hop distance, and the head should communicate with other cluster heads and pass all data to base station. For better communication between these cluster heads, lower maintenance cost, and easier management, it is necessary to make the number of the clusters as small as possible. Moreover, in many environments such as mountainous area or underwater monitoring, node deployment is often not flat, resulting in a high dimensional network. In this paper, we focus on proposing a scheme to select cluster heads for a homogeneous network in three-dimensional situation. The scheme meets two requirements: the number of cluster heads is minimum and the head nodes can communicate with each other. These requirements can be formed as an NP-complete problem named $d$ - hop connected dominating set . Correspondingly, we proposed a distributed approximation algorithm and proved its approximation ratio as $(d+1)\beta $ , where $\beta $ is a calculated parameter with respect to $d$ . We also analyzed the performance of our algorithm with corresponding numerical experiments.

A semi-supervised deep network embedding approach based on the neighborhood structure

Network embedding is a very important task to represent the high-dimensional network in a lowdimensional vector space, which aims to capture and preserve the network structure. Most existing network embedding methods are based on shallow models. However, actual network structures are complicated which means shallow models cannot obtain the high-dimensional nonlinear features of the network well. The recently proposed unsupervised deep learning models ignore the labels information. To address these challenges, in this paper, we propose an effective network embedding method of Structural Labeled Locally Deep Nonlinear Embedding (SLLDNE). SLLDNE is designed to obtain highly nonlinear features through utilizing deep neural network while preserving the label information of the nodes by using a semi-supervised classifier component to improve the ability of discriminations. Moreover, we exploit linear reconstruction of neighborhood nodes to enable the model to get more structural information. The experimental results of vertex classification on two real-world network datasets demonstrate that SLLDNE outperforms the other state-of-the-art methods.

High-dimensional structure learning of binary pairwise Markov networks: A comparative numerical study

Learning the undirected graph structure of a Markov network from data is a problem that has received a lot of attention during the last few decades. As a result of the general applicability of the model class, a myriad of methods have been developed in parallel in several research fields. Recently, as the size of the considered systems has increased, the focus of new methods has been shifted towards the high-dimensional domain. In particular, introduction of the pseudo-likelihood function has pushed the limits of score-based methods which were originally based on the likelihood function. At the same time, methods based on simple pairwise tests have been developed to meet the challenges arising from increasingly large data sets in computational biology. Apart from being applicable to high-dimensional problems, methods based on the pseudo-likelihood and pairwise tests are fundamentally very different. To compare the accuracy of the different types of methods, an extensive numerical study is performed on data generated by binary pairwise Markov networks. A parallelizable Gibbs sampler, based on restricted Boltzmann machines, is proposed as a tool to efficiently sample from sparse high-dimensional networks. The results of the study show that pairwise methods can be more accurate than pseudo-likelihood methods in settings often encountered in high-dimensional structure learning applications.

Topochemical Synthesis of Single-Crystalline Hydrogen-Bonded Cross-Linked Organic Frameworks and Their Guest-Induced Elastic Expansion.

Covalently linked single-crystalline porous organic materials are highly desired for structure-property analysis; however, periodically polymerizing organic entities into high dimensional networks is challenging. Here, we report a series of topologically divergent single-crystalline hydrogen-bonded cross-linked organic frameworks (HCOFs) with visible guest-induced elastic expansions, which mutually integrate high structural order and high flexibility into one framework. These HCOFs are synthesized by photo-cross-linking molecular crystals with alkyldithiols of different chain lengths. Their detailed structural information was revealed by single-crystal X-ray analysis and experimental investigations of HCOFs and their corresponding single-crystalline analogues. Upon guest adsorption, HCOF-2 crystals composed of a 3D self-entangled polymer network undergo anisotropic expansion to more than twice their original size, while the 2D-bilayer HCOF-3 crystals exhibit visible, layered sorption bands and form delaminated sheets along the plane of its 2D layers. The dynamic expansion of HCOF networks creates guest-induced porosity with over 473% greater volume than their permanent voids, as calculated from their record-breaking aqueous iodine adsorption capacities. Temperature-gated DMSO sorption investigations illustrated that the flexible nature of cross-linkers in HCOFs provides positive entropy from the coexistence of multiple conformations to allow for elastic expansion and contraction of the frameworks.

High-dimensional networks and spanning forests

High-dimensional networks are a topological generalization of electrical networks. As combinatorial invariants of electrical networks often require enumeration of trees, their high-dimensional analogues are also based on torsion-weighted enumeration of acyclic subcomplexes over the reals. In this paper, for a high-dimensional network with a current generator, we express a current vector and a voltage vector in terms of high-dimensional forests. To this end, we introduce a new simple method, an acyclization in codimension 1, for computing forest-numbers.

Dual-CISTs: Configuring a Protection Routing on Some Cayley Networks

A set of $k~(\geqslant 2)$ spanning trees in the underlying graph of a network topology is called completely independent spanning trees, (CISTs for short), if they are pairwise edge-disjoint and inner-node-disjoint. Particularly, if $k=2$ , the two CISTs are called a dual-CIST. However, it has been proved that determining if there exists a dual-CIST in a graph is an NP-hard problem. Kwong et al. [IEEE/ACM Transactions Networking 19(5) 1543–1556, 2011] defined that a routing is protected, if there is an alternate with loop-free forwarding, when a single link or node failure occurs. Shortly afterward, Tapolcai [Optim. Lett. 7(4) 723–730, 2013] showed that a network possessing a dual-CIST suffices to establish a protection routing. It is well-known that Cayley graphs have a large number of desirable properties of interconnection networks. Although many results of constructing dual-CISTs on interconnection networks have been proposed in the literature, so far, the work has not been dealt with on Cayley graphs due to that their expansions are in exponential scalability. In this paper, we try to make a breakthrough of this work on some famous subclasses of Cayley graphs, including alternating group networks, bubble-sort network, and star networks. We first propose tree searching algorithms for helping the construction of dual-CISTs on low-dimensional networks. Then, by inductive construction, we show that dual-CISTs on high-dimensional networks can also be constructed agreeably. As a result, we can configure protection routings by using the constructed dual-CISTs. In addition, we complement some analysis with a simulation study of the proposed construction to evaluate the corresponding performance.

Prognosis control surgery: From theory to practice

Rapid advances of big data and artificial intelligence (AI) techniques have pushed the envelope of traditional surgery to intelligent surgery, which revolutionizes the traditional medicine model dominated by the experiences of interveners and evidence-based medicine. Intelligent surgery requires to judiciously integrate the clinical experience of interveners and medical evidences with the new AI techniques, so as to achieve the best therapeutic effect for patients through effective disease risk control. This paper puts forward a new theory of prognostic control surgery in the long-term clinical practice of hepato-pancreato-biliary surgery. Our theory takes the optimal prognosis of patients as the goal, and pre-controls the disease risk through the best combination of the optimal intervener, intervention methods and intervention timing to achieve the maximum clinical benefits of patients with minimal medical trauma. This theory also takes full advantage of information technologies such as neural networks, deep learning, big data and imaging system, and uses high-dimensional network decision making to replace the traditional two-dimensional decision making tree model. A main technical challenge in the theory is how to effectively exploit the AI techniques in to improve the production efficiency of large hospitals, enhance the service level of primary medical care, and improve the diagnosis, prediction, treatment of diseases. Prognostic control surgery advocates the exploitation of emerging information technology methods, such as medical image recognition and prediction, 3D reconstruction based surgical planning, intraoperative navigation, and remote intelligent robotic surgical system, to promote the rapid and balanced surgical diagnosis and treatment. Guided by the theory of prognosis control surgery, our team successfully established minimally invasive anatomic hepatectomy, individualized pancreatic surgical approaches, modular hepatectomy, single-layer continuous suture of pancreaticojejunostomy, and end-to-end pancreatic anastomosis and advocated en-bloc resection of pancreatic cancer. This paper also provides the details of four core surgical strategies proposed in our prognosis control surgery, namely, blood control technique, surgical approach selection, resection technique and reconstruction technique, by which to achieve the minimally invasive surgery regularization and the complex surgery simplification.

The E. coli transcriptional regulatory network and its spatial embedding.

Usually complex networks are studied as graphs consisting of nodes whose spatial arrangement is of no significance. Several real biological networks are, however, embedded in space. In this paper we study the transcription regulatory network (TRN) of E. coli as a spatially embedded network. The embedding space of this network is the circular E. coli chromosome, i.e. it is practically one dimensional. However, the TRN itself is a high-dimensional network due to the existence of an adequate number of long-range connections. We find that nodes in short topological distance l = 1, 2 tend, on average, to be in shorter spatial distances r indicating an abundance of short-range connections as well. Community analysis of the TRN reveals the interesting fact that highly interconnected subnets consist of nodes that tend to be in spatial proximity on the circular chromosome. We also find indications that for certain transcriptional aspects of the E. coli it is advantageous to treat the circular genome as two line segments starting from the OriC and ending to Ter.

Multi-Noise and Multi-Channel Derived Prior Information for Grayscale Image Restoration

Image restoration is an extensively studied area with lots of outstanding algorithms developed. Nevertheless, most existing methods still have some limitations that only apply to a single tailored restoration task or suffer from long iterative reconstruction time or yield unstable results. To address these challenges, this work presents a multi-noise and multi-channel enhanced Deep Mean-Shift Prior (MEDMSP) for grayscale IR tasks. Specifically, we draw valuable high-dimensional prior knowledge by learning a multi-noise stimulated DMSP network from color images with RGB-channels. Variable augmentation technique is then adopted for incorporating the higher-dimensional network prior into the iterative reconstruction procedure. MEDMSP has been evaluated on different IR tasks and compared to a variety of state-of-the-art methods. Experimental results show that the proposed method has better capability in image deblurring and accurate compressive sensing reconstructions in terms of both visual and quantitative comparisons.

Firefly algorithm based feature selection for network intrusion detection

Network intrusion detection is the process of identifying malicious activity in a network by analyzing the network traffic behavior. Data mining techniques are widely used in Intrusion Detection System (IDS) to detect anomalies. Dimensionality reduction plays a vital role in IDS, since detecting anomalies from high dimensional network traffic feature is time-consuming process. Feature selection influences the speed of the analysis and the proposed work, deploys filter and wrapper based method with firefly algorithm in the wrapper for selecting the features. The resulting features are subjected to C4.5 and Bayesian Networks (BN) based classifier with KDD CUP 99 dataset. The experimental results show that 10 features are sufficient to detect the intrusion showing improved accuracy. The proposed work is compared with the existing work showing promising improvements.

Motor primitives in space and time via targeted gain modulation in cortical networks.

Motor cortex (M1) exhibits a rich repertoire of neuronal activities to support the generation of complex movements. Although recent neuronal-network models capture many qualitative aspects of M1 dynamics, they can generate only a few distinct movements. Additionally, it is unclear how M1 efficiently controls movements over a wide range of shapes and speeds. We demonstrate that modulation of neuronal input–output gains in recurrent neuronal-network models with fixed architecture can dramatically reorganize neuronal activity and thus downstream muscle outputs. Consistent with the observation of diffuse neuromodulatory projections to M1, a relatively small number of modulatory control units provide sufficient flexibility to adjust high-dimensional network activity using a simple reward-based learning rule. Furthermore, it is possible to assemble novel movements from previously learned primitives, and one can separately change movement speed while preserving movement shape. Our results provide a new perspective on the role of modulatory systems in controlling recurrent cortical activity.

Crystal and Molecular Structures of N-(5-Chloro-2-hydroxy-phenyl)-acetamide and Its Co-crystal with 3,5-Dinitrobenzoic Acid

Two crystalline compounds N-(5-chloro-2-hydroxy-phenyl)-acetamide [L] (1), and (N-(5-chloro-2-hydroxy-phenyl)-acetamide): (3,5-dinitrobenzoic acid) [(L) · (3,5-Hdns), 3,5-Hdns = 3,5-dinitrobenzoic acid] (2) were prepared and characterized by X-ray diffraction analysis, IR, mp, and elemental analysis. Compound 1 crystallizes in the monoclinic, space group C2/c, with a = 9.9833(7) A, b = 10.7789(8) A, c = 16.1622(14) A, β = 92.8010(10)°, V = 1737.1(2) A3, Z = 8. Compound 2 crystallizes in the monoclinic, space group C2/c, with a = 32.818(3) A, b = 6.9900(5) A, c = 14.8431(12) A, β = 90.5340(10)°, V = 3404.8(5) A3, Z = 8. Both supramolecular architectures of the compounds 1–2 involve N–H···O/O–H···O/C–H···O hydrogen bonds as well as other non-covalent association. The role of these non-covalent interactions in the crystal packing is ascertained. These weak interactions combined, the compounds displayed 1D–3D structures. The crystal structures of the N-(5-chloro-2-hydroxy-phenyl)-acetamide and its co-crystal with 3,5-dinitrobenzoic acid show the classical hydrogen bonding as well as CH–O, CH3–O, and π···π interactions, giving higher dimensional networks.

Multi-Scale Factor Analysis of High-Dimensional Functional Connectivity in Brain Networks

In this paper, we develop an approach to modeling high-dimensional networks with a large number of nodes arranged in a hierarchical and modular structure. We propose a novel multi-scale factor analysis (MSFA) model which partitions the massive spatio-temporal data defined over the complex networks into a finite set of regional clusters. To achieve further dimension reduction, we represent the signals in each cluster by a small number of latent factors. The correlation matrix for all nodes in the network are approximated by lower-dimensional sub-structures derived from the cluster-specific factors. To estimate regional connectivity between numerous nodes (within each cluster), we apply principal components analysis (PCA) to produce factors which are derived as the optimal reconstruction of the observed signals under the squared loss. Then, we estimate global connectivity (between clusters or sub-networks) based on the factors across regions using the RV-coefficient as the cross-dependence measure. This gives a reliable and computationally efficient multi-scale analysis of both regional and global dependencies of the large networks. The proposed novel approach is applied to estimate brain connectivity networks using functional magnetic resonance imaging (fMRI) data. Results on resting-state fMRI reveal interesting modular and hierarchical organization of human brain networks during rest.