Local Topological Structure Research Articles

LTSA-LE: A local tangent space alignment label enhancement algorithm

According to smoothness assumption, local topological structure can be shared between feature and label manifolds. This study proposes a new algorithm based on Local Tangent Space Alignment (LTSA) to implement the label enhancement process. In general, we first establish a learning model for feature extraction in label space and use a feature extraction method of LTSA to guide the reconstruction of label manifolds. Then, we establish an unconstrained optimization model based on the optimal theory presented in this paper. The model is suitable for solving problems with a large number of sample points. Finally, the experiment results show that the algorithm can effectively improve the training speed and multilabel dataset prediction accuracy.

Geometry consistency aware confidence evaluation for feature matching

Most existing approaches prune wrong matches via estimating an image transformation or solving a graph-based global matching optimization problem, which usually suffers from varying local transformations and outliers. Inspired by the insight that neighboring true matches usually hold consistent local topological structures across images, in this paper we propose a new approach to evaluate the confidence of each putative match based on how well its two keypoints can predict each other by exploring the geometric constraint with its neighboring matches. With the evaluation, a two-stage approach combining recursively false match pruning and correct match incrementing is presented to obtain the reliable matches. Experiments on various image pairs demonstrate that our approach can conduct robust feature matching in challenging conditions and outperform state-of-the-art approaches.

Local k-NNs pattern in Omni-Direction graph convolution neural network for 3D point clouds

Effective representation of objects in irregular and unordered point clouds is one of the core challenges in 3D vision. Transforming point cloud into regular structures, such as 2D images and 3D voxels, are not ideal. It either obscures the inherent geometry information of 3D data or results in high computational complexity. Learning permutation invariance feature directly from raw 3D point clouds using deep neural network is a trend, such as PointNet and its variants, which are effective and computationally efficient. However, these methods are weak to reveal the spatial structure of 3D point clouds. Our method is delicately designed to capture both global and local spatial layout of point cloud by proposing a Local k-NNs Pattern in Omni-Direction Graph Convolution Neural Network architecture, called LKPO-GNN. Our method converts the unordered 3D point cloud into an ordered 1D sequence, to facilitate feeding the raw data into neural networks and simultaneously reducing the computational complexity. LKPO-GNN selects multi-directional k-NNs to form the local topological structure of a centroid, which describes local shapes in the point cloud. Afterwards, GNN is used to combine the local spatial structures and represent the unordered point clouds as a global graph. Experiments on ModelNet40, ShapeNetPart, ScanNet, and S3DIS datasets demonstrate that our proposed method outperforms most existing methods, which verifies the effectiveness and advantage of our work. Additionally, a deep analysis towards illustrating the rationality of our approach, in terms of the learned the topological structure feature, is provided. Source code is available at https://github.com/zwj12377/LKPO-GNN.git.

Unsupervised nonlinear adaptive manifold learning for global and local information

In this paper, we propose an Unsupervised Nonlinear Adaptive Manifold Learning method (UNAML) that considers both global and local information. In this approach, we apply unlabeled training samples to study nonlinear manifold features, while considering global pairwise distances and maintaining local topology structure. Our method aims at minimizing global pairwise data distance errors as well as local structural errors. In order to enable our UNAML to be more efficient and to extract manifold features from the external source of new data, we add a feature approximate error that can be used to learn a linear extractor. Also, we add a feature approximate error that can be used to learn a linear extractor. In addition, we use a method of adaptive neighbor selection to calculate local structural errors. This paper uses the kernel matrix method to optimize the original algorithm. Our algorithm proves to be more effective when compared with the experimental results of other feature extraction methods on real face-data sets and object data sets.

Surface anchoring as a control parameter for stabilizing torons, skyrmions, twisted walls, fingers, and their hybrids in chiral nematics.

Chiral condensed matter systems, such as liquid crystals and magnets, exhibit a host of spatially localized topological structures that emerge from the medium's tendency to twist and its competition with confinement and field coupling effects. We show that the strength of perpendicular surface boundary conditions can be used to control the structure and topology of solitonic and other localized field configurations. By combining numerical modeling and three-dimensional imaging of the director field, we reveal structural stability diagrams and intertransformation of twisted walls and fingers, torons, and skyrmions and their crystalline organizations upon changing boundary conditions. Our findings provide a recipe for controllably realizing skyrmions, torons, and hybrid solitonic structures possessing features of both of them, which will aid in fundamental explorations and technological uses of such topological solitons. Moreover, we discuss how other material parameters can be used to determine soliton stability and how similar principles can be systematically applied to other liquid crystal solitons and solitons in other material systems.

Geometrical particles and Legendrian dualities related to null curves

In this paper, we investigate the special properties of geometrical particles with null paths in de Sitter 3-space–time, new Frenet equations and an important invariant associated with null paths are presented. By means of unfolding theory, the local topological structure of the lightlike dual surfaces is revealed. It is found that the lightlike dual surface has some singularities whose types can be determined by the invariant. Based on the theory of Legendrian dualities on pseudospheres and the theory of contact manifolds, it is shown that there exists the [Formula: see text]-dual relationship between the lightlike transversal trajectory of the particle and the lightlike dual surface. In addition, an interesting and important fact mentioned is that the contact of lightlike transversal trajectory with lightcone quadric and the contact of lightlike transversal trajectory with null hyperplane have the same order when they are related to the same type of singularities of the lightlike dual surface.

On the role of local blockchain network features in cryptocurrency price formation

AbstractCryptocurrencies and the underpinning blockchain technology have gained unprecedented public attention recently. In contrast to fiat currencies, transactions of cryptocurrencies, such as Bitcoin and Litecoin, are permanently recorded on distributed ledgers to be seen by the public. As a result, public availability of all cryptocurrency transactions allows us to create a complex network of financial interactions that can be used to study not only the blockchain graph, but also the relationship between various blockchain network features and cryptocurrency risk investment. We introduce a novel concept of chainlets, or blockchain motifs, to utilize this information. Chainlets allow us to evaluate the role of local topological structure of the blockchain on the joint Bitcoin and Litecoin price formation and dynamics. We investigate the predictive Granger causality of chainlets and identify certain types of chainlets that exhibit the highest predictive influence on cryptocurrency price and investment risk. More generally, while statistical aspects of blockchain data analytics remain virtually unexplored, the paper aims to highlight various emerging theoretical, methodological and applied research challenges of blockchain data analysis that will be of interest to the broad statistical community. The Canadian Journal of Statistics 48: 561–581; 2020 © 2020 Statistical Society of Canada

Using Alias Sampling Strategy Based on Network Embeddings to Detect Protein Complexes

Detecting protein complexes from available protein-protein interaction (PPI) data will help to deeply understand the mechanism of the biological activities. In recent years, various computational methods have been developed for identifying protein complexes from PPI networks. Almost all the basic computational methods mainly depend on the association of topological analysis of PPI networks. However, most of them fail to satisfactorily capture the global and local topological structures of the PPI networks, as well as the diversity of connectivity patterns between individual nodes at the same time. To solve this problem, in this work we propose a node embedding based alias sampling extension method to detect protein complexes. More specifically, for a given set of seed nodes, it first uses the alias sampling strategy based on protein node embedding similarities to select potential addable nodes. Then it makes use of a new conductance measure, which could better quantify the likelihood of a subgraph being a protein complex, to decide whether to extend the current candidate subgraph in order to find protein complexes. Evaluated on six real yeast PPI networks, our method outperforms state-of-the-art methods in detecting protein complexes. Furthermore, the experimental results demonstrate the protein complexes predicted by our method have higher biological significance.

Local Structure and High-Order Feature Preserved Network Embedding Based on Non-Negative Matrix Factorization

Network embedding, as an effective method of learning the low-dimensional representations of nodes, has been widely applied to various complex network analysis tasks, such as node classification, community detection, link prediction and evolution analysis. The existing embedding methods usually focus on the local structure of the network by capturing community structure, first-order or second-order proximity, etc. Some methods have been proposed to model the high-order proximity of networks to capture more effective information. However, they are incapable of preserving the similarity among nodes that are not very close to each other in network but have similar structures. For instance, the nodes with similar local topology structure should be similar in embedding space even if they are not in the same community. Herein, we regard these structure characteristics as the high-order features, which reveals that the structure similarity between nodes is spatially unrelated. In light of above the limitations of existing methods, we construct the high-order feature matrix for mutually reinforcing the embedding which preserves the local structure. To integrate these features effectively, we propose LHO-NMF, which fuses the high-order features into non-negative matrix factorization framework while capturing the local structure. The proposed LHO-NMF could effectively learn the node representations via preserving the local structure and high-order feature information. In specific, the high-order features are learned based on random walk algorithm. The experimental results show that the proposed LHO-NMF method is very effective and outperforms other state-of-the-art methods among multiple downstream tasks.

Mutual-manifold regularized robust fast latent LRR for subspace recovery and learning

In this paper, we propose a simple yet effective low-rank representation (LRR) and subspace recovery model called mutual-manifold regularized robust fast latent LRR. Our model improves the representation ability and robustness from twofold. Specifically, our model is built on the Frobenius norm-based fast latent LRR decomposing given data into a principal feature part, a salient feature part and a sparse error, but improves it clearly by designing mutual-manifold regularization to encode, preserve and propagate local information between coefficients and salient features. The mutual-manifold regularization is defined by using the coefficients as the adaptive reconstruction weights for salient features and constructing a Laplacian matrix over salient features for the coefficients. Thus, some important local topology structure information can be propagated between them, which can make the discovered subspace structures and features potentially more accurate for the data representations. Besides, our approach also considers to improve the robust properties of subspace recovery against noise and sparse errors in coefficients, which is realized by decomposing original coefficients matrix into an error-corrected part and a sparse error part fitting noise in coefficients, and the recovered coefficients are then used for robust subspace recovery. Experimental results on several public databases demonstrate that our method can outperform other related algorithms.

Spontaneous and engineered transformations of topological structures in nonlinear media with gain and loss.

In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures exhibit many unique features that can be controlled externally. We propose a robust mechanism to perform topological transformations changing characteristics of dissipative vortices and their complexes in a controllable way. We show that a properly chosen potential carries out the evolution of dissipative structures to regime with spontaneous transformation of the topological excitations or drives generation of vortices with control over the topological charge.

Adequate mathematical modelling by wide-sense robust control design in a thrust-vectored flight dynamics problem

The conflict between the accuracy and the complexity of the adequate mathematical modelling approximations of physical phenomena is discussed. The need of finding certain types of topological equivalency between nonlinear mathematical models as the keystone to successful study is emphasized. We formulate the control problem when the controlling functions cannot directly act on the phase variables defining a given terminal manifold as a control aim through the right-hand sides of differential equations describing a mathematical model under study. The idea of creating a hierarchical cascade of controlling attractors–mediators is introduced. It is shown how the method of the goal-oriented formation of the local topological structure of one-codimensional foliations as the basis of Poincare’s-strategy-based backstepping method can be successfully used for designing terminal control. One brings up the problem of developing the tools intended for the creation of the topologically equivalent and quantitative–deviation–tolerable simplifications of the complex original mathematical models suitable for the synthesis of the control laws that are supposed to be applied to the latter ones. The two-dimensional example is analytically investigated to explain the procedure of constructing the cascade of controlling one-codimensional attractor mediators. The essentially nonlinear five-dimensional mathematical model of the longitudinal flight dynamics of a thrust-vectored aircraft in a wing-body coordinate system with two controls, namely, the angular deflections of a movable horizontal stabilizer and a turbojet engine nozzle, is investigated. The core of the designed wide-sense robust and stable in the large-tracking control algorithm is a hierarchical cascade of controlling attractor–mediators consisting of the two one-codimensional manifolds. The results of the computer simulation are presented. The topicality in creating the general theory of nonlinear mathematical modelling, as the tools to construct and manipulate the sets of topologically equivalent models being qualitative–quantitative adequate to corresponding physical phenomena, is pointed up in conclusion.

A two-route CNN model for bank account classification with heterogeneous data.

Classifying bank accounts by using transaction data is encouraging in cracking down on illegal financial activities. However, few research simultaneously use heterogenous features, which are embedded in the time series data. In this paper, a two route convolution neural network TRHD-CNN model, fed with two types of heterogeneous feature matrices, is proposed for classifying the bank accounts. TRHD-CNN adopts divide and conquer strategy to extract characteristics from two types of data source independently. The strategy is proved able in mining complementary classification characteristics. We firstly transfer the original log data into a directed and dynamic transaction network. On the basis of that, two feature generation methods are devised for extracting information from local topological structure and time series transaction respectively. A DirectedWalk method is developed in this paper to learning the network vector of vertices used for embedding the neighbor relationship of bank account. The extensive experimental results, conducted on a real bank transaction dataset that contains illegal pyramid selling accounts, show the significant advantage of TRHD-CNN over the existing methods. TRHD-CNN can provide recall scores up to 5.15% higher than competing methods. In addition, the two-route architecture of TRHD-CNN is easy to extend to multi-route scenarios and other fields.

Utility analysis on privacy-preservation algorithms for online social networks: an empirical study

Social networks have gained tremendous popularity recently. Millions of people use social network apps to share precious moments with friends and family. Users are often asked to provide personal information such as name, gender, and address when using social networks. However, as the social network data are collected, analyzed, and re-published at a large scale, personal information might be misused by unauthorized third parties and even attackers. Therefore, extensive research has been carried out to protect the data from privacy violations in social networks. The most popular technique is graph perturbation, which modifies the local topological structure of a social network user (a vertex) via various randomization techniques before the social graph data is published. Nevertheless, graph anonymization may affect the usability of the data as random noises are introduced, decreasing user experience. Therefore, a trade-off between privacy protection and data usability must be sought. In this paper, we employ various graph and application utility metrics to investigate this trade-off. More specifically, we conduct an empirical study by implementing five state-of-the-art anonymization algorithms to analyze the graph and application utilities on a Facebook and a Twitter dataset. Our results indicate that most anonymization algorithms can partially or conditionally preserve the graph and application utilities and any single anonymization algorithm may not always perform well on different datasets. Finally, drawing on the reviewed graph anonymization techniques, we provide a brief overview on future research directions and challenges involved therein.

LKLR: A local tangent space-alignment kernel least-squares regression algorithm

In the fields of machine learning and data mining, label learning is a nascent area of research, and within this paradigm, there is much room for improving multi-label manifold learning algorithms for high-dimensional data. Thus far, researchers have experimented with mapping relationships from the feature space to the traditional logical label space (using neighbors in the label space, for example, to predict logical label vectors from the feature space's manifold structure). Here we combine the feature manifold's and label space's local topological structures to reconstruct the label manifold. To achieve this, we use a nonlinear manifold learning algorithm to transform the local topological structure from the feature space to the label space. Our algorithm adopts a regularized least-squares kernel method to realize the reconstruction process, employing an optimization function to find the best solution. Extensive experiments show that our algorithm significantly improves multi-label manifold learning in terms of learning accuracy and time complexity.

Topology-based characterization of compressibility effects in mixing layers

Direct numerical simulations of high-speed mixing layers are used to characterize the effects of compressibility on the basis of local streamline topology and vortical structure. Temporal simulations of the mixing layers are performed using a finite volume gas-kinetic scheme for convective Mach numbers ranging from $M_{c}=0.2$ to $M_{c}=1.2$. The focus of the study is on the transient development and the main objectives are to (i) investigate and characterize the turbulence suppression mechanism conditioned upon local streamline topology; and (ii) examine changes in the vortex vector field – distribution, magnitude and orientation – as a function of Mach number. We first reaffirm that kinetic energy suppression with increasing Mach number is due to a decrease in pressure–strain redistribution. Then, we examine the suppression mechanism conditioned upon topology and vortex structure. Conditional statistics indicate that (i) at a given Mach number, shear-dominated topologies generally exhibit more effective pressure–strain redistribution than vortical topologies; and (ii) for a given topology, the level of pressure–strain correlation mostly decreases with increasing Mach number. At each topology, with increasing Mach number, there is a corresponding decrease in turbulent shear stress and production leading to reduced kinetic energy. Further, as $M_{c}$ increases, the proportion of vortex-dominated regions in the flow increases, leading to further reduction in the turbulent kinetic energy of the flow. Then, the orientation of vortical structures and direction of fluid rotation are examined using the vortex vector approach of Tian et al. (J. Fluid Mech., vol. 849, 2018, pp. 312–339). At higher $M_{c}$, the vortex vectors tend to be more aligned in the streamwise direction in contrast to low $M_{c}$ wherein larger angles with streamwise direction are preferred. The connection between vortex orientation and kinetic energy production is also investigated. The findings lead to improved insight into turbulence suppression dynamics in high Mach number turbulent flows.

Detecting evolving communities in dynamic networks using graph regularized evolutionary nonnegative matrix factorization

Many networks in society and nature are dynamic, and identifying evolving communities in dynamic networks sheds light on revealing the structure and function of the overall systems. Evolutionary clustering is based on the temporal smoothness framework that simultaneously maximizes the clustering accuracy at the current time step and minimizes the clustering drift between two successive time steps. However, they are criticized for the linear combination of networks at two successive time steps because the relation between networks is unnecessary linear. To address this problem, we propose the Graph regularized Evolutionary Nonnegative Matrix Factorization algorithm (GrENMF) for the dynamic community detection, where the network at the previous time step is transformed as a regularizer into the objective function. Moreover, the local topological structure in the network at the previous time step is preserved in communities at the current time step, which improves the performance of algorithm without increasing the time complexity. Furthermore, we prove the equivalence among evolutionary nonnegative matrix factorization (ENMF), spectral clustering, kernel K-means, modularity density and GrENMF, which serves as the theoretical foundation for the GrENMF algorithm. The experimental results over a number of artificial and real world dynamic networks illustrate that the proposed method is not only more accurate, but also more robust than state-of-the-art approaches.

НЕОБРАТИМЫЙ ГИСТЕРЕЗИС ТРЕХМЕРНЫХ ТОПОЛОГИЧЕСКИХ ЗАПУТАННЫХ ЛАЗЕРНЫХ СОЛИТОНОВ

In a laser medium with saturable amplification and absorption or in a laser with such a medium and a sufficiently large cavity length, the authors previously demonstrated a class of dissipative three-dimensional topological solitons (Veretenov et al., 2016, 2017). Such solitons have “skeletons” – a set of several closed and unclosed vortex lines, on which the field turns to 0 and the phase of which bypass is incremented by a multiple of 2π. It is significant that the regions of the scheme parameters in which different types of topological solitons exist and are stable, overlap. Accordingly, the question arises about the nature of changes in the structure of solitons and their skeletons with a slow change in the parameters. The answer to this question, mainly in the framework of numerical modeling, is the subject of this report. The initial equation is the generalized Ginzburg-Landau complex equation for a slowly varying envelope of the field, with the longitudinal coordinate along the path of preferential propagation z (Veretenov et al., 2017) serving as an evolution variable. The control parameter is the coefficient of linear (unsaturated) field gain g0. The initial value of this parameter corresponds to the central part of the stability region of the original soliton (for definiteness, the “Solomon soliton”). Then g0 slowly increases, crossing the stability boundary, after which it stabilizes and slowly decreases, eventually returning to its original value. We demonstrate that as a result of such a hysteresis cycle, the soliton does not return to the initial one — its structure is drastically simplified. This is reflected in a decrease in the values of various topological indices, as well as in a decrease in the field energy and an increase in the energy of the active medium (minus its constant background). At the g0 reduction stage, the topological characteristics do not change (two “soliton-apples”). The transient process includes a series of elementary reactions of reconnection of the vortex lines and detachment of closed loops after a strong bend of the “parent” vortex line. In addition, during the transition process, a number of new types of localized topological metastable structures arise. The analytical part of the research was supported by the RAS Presidium Program “Nonlinear Dynamics: Fundamental Problems and Applications”. Numerical modeling was carried out with the support of the grant of the RNF 18-12-00075.

Topology-aware non-rigid point set registration via global–local topology preservation

We propose a new topology-aware point set registration algorithm which can cope with multi-part articulated and non-rigid deformations. Point set registration is formulated as a maximum likelihood (ML) estimation problem where two topologically complementary constraints are jointly optimized in a probabilistic framework. The first is coherent point drift that keeps the overall spatial connectivity and associativity by moving the point set collectively and coherently. The second is local linear embedding that preserves the local topological structure during registration. Hence, the new algorithm is called global–local topology preservation (GLTP). Without any pre-segmentation and correspondence initialization, GLTP is particularly useful and effective in dealing with complex shape matching with non-coherent and non-rigid local deformations at different parts of a point set. We have derived the expectation maximization algorithm for the ML optimization constrained with both regularization terms. Experimental results on a large set of 2D and 3D examples show the advantages and robustness of GLTP over existing algorithms in the presence of outliers, noise and missing data, especially in the case of articulated non-rigid transformations.

Diagnosis of Brain Diseases via Multi-Scale Time-Series Model.

The functional magnetic resonance imaging (fMRI) data and brain network analysis have been widely applied to automated diagnosis of neural diseases or brain diseases. The fMRI time series data not only contains specific numerical information, but also involves rich dynamic temporal information, those previous graph theory approaches focus on local topology structure and lose contextual information and global fluctuation information. Here, we propose a novel multi-scale functional connectivity for identifying the brain disease via fMRI data. We calculate the discrete probability distribution of co-activity between different brain regions with various intervals. Also, we consider nonsynchronous information under different time dimensions, for analyzing the contextual information in the fMRI data. Therefore, our proposed method can be applied to more disease diagnosis and other fMRI data, particularly automated diagnosis of neural diseases or brain diseases. Finally, we adopt Support Vector Machine (SVM) on our proposed time-series features, which can be applied to do the brain disease classification and even deal with all time-series data. Experimental results verify the effectiveness of our proposed method compared with other outstanding approaches on Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and Major Depressive Disorder (MDD) dataset. Therefore, we provide an efficient system via a novel perspective to study brain networks.