Undirected Graph Structure Research Articles

Classification Model of 3D Point Cloud Based on Linked Adaptive Graph Convolution

A three-dimensional point cloud classification model LAGCN based on adaptive graph convolution is proposed to solve the problem that PointNet only extracts feature information from isolated points but not from neighborhood structure. Firstly, the three-dimensional point cloud is transformed into undirected graph structure, which is used to obtain the neighborhood information of point cloud adaptively, and the classification accuracy is improved by incorporating residual structure. In the classification experiment, this paper trains and tests on ModelNet40 dataset, and compares the classification accuracy with VoxNet, PointNet and DGCNN models. The classification accuracy of this model is better than that of the above models.

Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling

In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying (undirected) graph structure. The proposed coupling law is motivated by the so-called funnel control method studied in adaptive control under the observation that arbitrary precision synchronization can be achieved for heterogeneous multi-agent systems by a high-gain coupling; consequently we call our novel synchronization method ‘(node-wise) funnel coupling.’ By adjusting the conventional proof technique in the funnel control study, we are even able to obtain asymptotic synchronization with the same funnel coupling law. Moreover, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, is analyzed in this paper. In particular, we introduce a single scalar dynamics called ‘emergent dynamics’ which describes the emergent synchronized behavior of the multi-agent system under funnel coupling. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. We illustrate this idea via the example of a distributed median solver based on funnel coupling.

Evolutionary Exploration of Mechanical Assemblies in VR

Due to the maker movement and 3D printers, people nowadays can directly fabricate mechanical devices that meet their own objectives. However, it is not intuitive to identify the relationship between specific mechanical movements and mechanical structures that facilitate such movements. This paper presents an interactive system that can enable users to easily create and experiment with desired mechanical assemblies via direct manipulation interfaces in virtual reality, as well as to intuitively explore design space through repeated application of the crossover operation, which is used at the core of the genetic algorithm. Specifically, a mechanical assembly in our system is genetically encoded as a undirected graph structure in which each node corresponds to a mechanical part and each edge represents the connection between parts. As the user selects two different mechanical assemblies and commands the crossover operation, each of their corresponding graphs is split into two subgraphs and those subgraphs are recombined to generate the next-generation mechanical assemblies. The user can visually examine new mechanical assemblies, save assemblies that are closer to objectives, and remove the others. Based on our experiments, in which non-expert participants were asked to achieve a challenging design objective, it was verified that the proposed interface exhibited significantly effective performance.

A New Framework for Smartphone Sensor-Based Human Activity Recognition Using Graph Neural Network

Automatic human activity recognition (HAR) through computing devices is a challenging research topic in the domain of computer vision. It has widespread applications in various fields such as sports, healthcare, criminal investigation and so on. With the advent of smart devices like smartphones, availability of inertial sensors like accelerometer and gyroscope can easily be used to track our daily physical movements. State-of-the-art deep neural network models like Convolutional Neural Network (CNN) do not need any additional feature extraction for such applications. However, it requires huge amount of data for training which is time consuming, and requires ample resource. Another limiting factor of CNN is that it considers only the features of an individual sample for learning without considering any structural information among the samples. To address the aforesaid issues, we propose an end-to-end fast Graph Neural Network (GNN) which not only captures the individual sample information efficiently but also the relationship with other samples in the form of an undirected graph structure. To the best of our knowledge, this is the first work where the time series data are transformed into a structural representation of graph for the purpose of HAR using sensor data. Proposed model has been evaluated on 6 publicly available datasets, and it achieves nearly 100% recognition accuracy for all the 6 datasets. Source code of this work is available at https://github.com/riktimmondal/HAR-Sensor.

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.

HoTPiG: a novel graph-based 3-D image feature set and its applications to computer-assisted detection of cerebral aneurysms and lung nodules.

A novel image feature set named histogram of triangular paths in graph (HoTPiG) is presented. The purpose of this study is to evaluate the feasibility of the proposed HoTPiG feature set through two clinical computer-aided detection tasks: nodule detection in lung CT images and aneurysm detection in head MR angiography images. The HoTPiG feature set is calculated from an undirected graph structure derived from a binarized volume. The features are derived from a 3-D histogram in which each bin represents a triplet of shortest path distances between the target node and all possible node pairs near the target node. First, the vessel structure is extracted from CT/MR volumes. Then, a graph structure is extracted using an 18-neighbor rule. Using this graph, a HoTPiG feature vector is calculated at every foreground voxel. After explicit feature mapping with an exponential-χ2 kernel, each voxel is judged by a linear support vector machine classifier. The proposed method was evaluated using 300 CT and 300 MR datasets. The proposed method successfully detected lung nodules and cerebral aneurysms. The sensitivity was about 80% when the number of false positives was three per case for both applications. The HoTPiG image feature set was presented, and its high general versatility was shown through two medical lesion detection applications.

3D Object Retrieval Based on Multi-View Latent Variable Model

View-based 3D object retrieval, in which multiple views are used for representation and retrieval, has attracted increasing attention due to its great flexibility. In this paper, we propose a discriminative multi-view latent variable model (MVLVM) for this task. Specifically, we design MVLVM to have an undirected graph structure in which the view set of a given 3D object is treated as the observations from which to discover the latent visual and spatial contexts. Then, we detail the learning and inference process of MVLVM for view-based 3D object retrieval. The proposed MVLVM has the following beneficial features: 1) it jointly learns visual and spatial contexts for 3D object modelling and 2) it avoids the difficulty of representative view extraction for model representation. Consequently, it can support flexible 3D model retrieval for real applications by avoiding camera array constraints, which severely constrain traditional methods. We report extensive experiments conducted on single-modal datasets (the NTU and ITI datasets) and a multi-modal dataset (MVRED-RGB and MVRED-Depth). These comparative experiments demonstrate the superiority of the proposed method.

Evolutionary regime transitions in structured populations.

The evolutionary dynamics of a finite population where resident individuals are replaced by mutant ones depends on its spatial structure. Usually, the population adopts the form of an undirected graph where the place occupied by each individual is represented by a vertex and it is bidirectionally linked to the places that can be occupied by its offspring. There are undirected graph structures that act as amplifiers of selection increasing the probability that the offspring of an advantageous mutant spreads through the graph reaching any vertex. But there also are undirected graph structures acting as suppressors of selection where this probability is less than that of the same individual placed in a homogeneous population. Here, firstly, we present the distribution of these evolutionary regimes for all undirected graphs with N ≤ 10 vertices. Some of them exhibit transitions between different regimes when the mutant fitness increases. In particular, as it has been already observed for small-order random graphs, we show that most graphs of order N ≤ 10 are amplifiers of selection. Secondly, we describe examples of amplifiers of order 7 that become suppressors from some critical value. In fact, for graphs of order N ≤ 7, we apply computer-aided techniques to symbolically compute their fixation probability and then their evolutionary regime, as well as the critical values for which they change their regime. Thirdly, the same technique is applied to some families of highly symmetrical graphs as a mean to explore methods of suppressing selection. The existence of suppression mechanisms that reverse an amplification regime when fitness increases could have a great interest in biology and network science. Finally, the analysis of all graphs from order 8 to order 10 reveals a complex and rich evolutionary dynamics, with multiple transitions between different regimes, which have not been examined in detail until now.

The Lyapunov–Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators

This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov–Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov–Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua’s circuit, Van der Pol oscillator and the Hindmarsh–Rose neuron.

Closure operators associated with networks

We study network (i.e., undirected simple graph) structures by investigating associated closure operators and the corresponding closed sets. To describe the dynamic behavior of networks, we employ continuous transformations and neighborhood homomorphisms between them. These transformations and homomorphisms are then studied. In particular, the problem of preserving generators by continuous transformations and that of preserving minimal dominating sets by neighborhood homomorphisms are dealt with.

A unified framework for harmonic analysis of functions on directed graphs and changing data

We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of the now classical diffusion geometry approach is the construction of a kernel whose discretization leads to an undirected graph structure on an unstructured data set. We study the question of constructing such kernels for directed graph structures, and argue that our construction is essentially the only way to do so using discretizations of kernels. We then use our previous theory to develop harmonic analysis based on the singular value decomposition of the resulting non-self-adjoint operators associated with the directed graph. Next, we consider the question of how functions defined on one space evolves to another space in the paradigm of changing data sets recently introduced by Coifman and Hirn. While the approach of Coifman and Hirn require that the points on one space should be in a known one-to-one correspondence with the points on the other, our approach allows the identification of only a subset of landmark points. We introduce a new definition of distance between points on two spaces, construct localized kernels based on the two spaces and certain interaction parameters, and study the evolution of smoothness of a function on one space to its lifting to the other space via the landmarks. We develop novel mathematical tools that enable us to study these seemingly different problems in a unified manner.

Completely Described Undirected Graph Structure

Completely Described Undirected Graph Structure

Optimization Mode Research of Weighted Undirected Graph

An algorithm is described for constructing a weighted undirected graph structure, based on the principle of directed acyclic graph, used the improved Floyd algorithm to improve the multi-node version of the evolution of information in order to release as an indicator of difference, to improve the reliability of multiple versions of data storage and multi-version storage and query efficiency. Theory and examples show that efficiency is improved using the optimization model in multi-node information system.

Graph-based multilevel temporal video segmentation

This paper presents a graph-based multilevel temporal video segmentation method. In each level of the segmentation, a weighted undirected graph structure is implemented. The graph is partitioned into clusters which represent the segments of a video. Three low-level features are used in the calculation of temporal segments' similarities: visual content, motion content and shot duration. Our strength factor approach contributes to the results by improving the efficiency of the proposed method. Experiments show that the proposed video scene detection method gives promising results in order to organize videos without human intervention.