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Different from other computer vision tasks, action recognition needs to process larger-scale video data. How to extract and analyze the effective parts from a huge amount of video information is the main difficulty of action recognition technology. In recent years, due to the outstanding performance of Graph Convolutional Networks (GCN) in many fields, a new solution to the action recognition algorithm has emerged. However, in current GCN models, the constant physical adjacency matrix makes it difficult to mine synergistic relationships between key points that are not directly connected in physical space. Additionally, a simple time connection of skeleton data from different frames makes each frame in the video contribute equally to the recognition results, which increases the difficulty of distinguishing action stages. In this paper, the information extraction ability of the model has been optimized in the space domain and time domain, respectively. In the space domain, an Adjacency Matrix Generation (AMG) module, which can pre-analyze node sets and generate an adaptive adjacency matrix, has been proposed. The adaptive adjacency matrix can help the graph convolution model to extract the synergistic information between the key points that are crucial for recognition. In the time domain, the Time Domain Attention (TDA) mechanism has been designed to calculate the time-domain weight vector through double pooling channels and complete the weights of key point sequences. Furthermore, performance of the improved TDA-AMG-GCN modules has been verified on the NTU-RGB+D dataset. Its detection accuracy at the CS and CV divisions reached 84.5% and 89.8%, respectively, with an average level higher than other commonly used detection methods at present.

The traditional method of searching transmission section generally has the problem of omission and time-consuming. A topology converging algorithm of power grid adjacency matrix is proposed in this paper. It aggregates neighboring buses based on a simple matrix transformation rule, and identify key transmission sections based on matrix operations and power flow distribution factors. This method has the advantage of no presetting the sub-zone, which can avoid the simplification of the grid topology in the sub-zone and improve the calculation accuracy. The complex logical operations of the traversal algorithm adopted by most of traditional methods can be avoided, and the calculation speed can be effectively improved. Besides, the algorithm also has a memory characteristic which can be applied to the online search of key transmission sections. The results of several IEEE test systems show the effectiveness of the proposed algorithm.

Accurate forecasting of taxi demand has facilitated the rational allocation of urban public transport resources, reduced congestion in urban transport networks, and shortened passenger waiting time. However, virtual station discovery and modelling of the demand when forecasting through graph convolutional neural networks remains challenging. In this study, the virtual station discovery problem was addressed by using a two-stage clustering approach, which considers the geographical and load characteristics of taxi demand. Furthermore, a fusion model combining non-negative matrix decomposition and a graph convolutional neural network was proposed in order to extract the features of the nodes for dimension reduction and adaptive adjacency matrix computation. By the construction of a local processing structure, further extraction of the local characteristics of the demand was achieved. The experimental results show that the method in this study outperforms state-of-the-art methods in terms of the root mean square error and average absolute value error. Therefore, the model proposed in this study is able to achieve accurate forecasting of taxi demand.

Image clustering is a research hotspot in machine learning and computer vision. Existing graph-based semi-supervised deep clustering methods suffer from three problems: 1) because clustering uses only high-level features, the detailed information contained in shallow-level features is ignored; 2) most feature extraction networks employ the step odd convolutional kernel, which results in an uneven distribution of receptive field intensity; and 3) because the adjacency matrix is precomputed and fixed, it cannot adapt to changes in the relationship between samples. To solve the above problems, we propose a novel graph-based semi-supervised deep clustering method for image clustering. First, the parity cross-convolutional feature extraction and fusion module is used to extract high-quality image features. Then, the clustering constraint layer is designed to improve the clustering efficiency. And, the output layer is customized to achieve unsupervised regularization training. Finally, the adjacency matrix is inferred by actual network prediction. A graph-based regularization method is adopted for unsupervised training networks. Experimental results show that our method significantly outperforms state-of-the-art methods on USPS, MNIST, street view house numbers (SVHN), and fashion MNIST (FMNIST) datasets in terms of ACC, normalized mutual information (NMI), and ARI.

There are many types of planetary gear trains， and each one corresponds to a transmission ratio calculation formula， which makes great difficulties in the comprehensive research of planetary gear trains and the development of general design software. According to the structural diagram of the planetary gear train， the corresponding adjacency matrix is written. Then， the basic loop of the train is searched from the adjacency matrix to construct the basic loop matrix. Finally， the basic loop matrix is transformed into the coefficient matrix of the equation of motion. And use MATLAB to automate this algorithm and solve the equation of motion to obtain the gear ratio of the planetary gear train.

The paper presents a novel spectral algorithm EVSA (eigenvector structure analysis), which uses eigenvalues and eigenvectors of the adjacency matrix in order to discover clusters. Based on matrix perturbation theory and properties of graph spectra we show that the adjacency matrix can be more suitable for partitioning than other Laplacian matrices. The main problem concerning the use of the adjacency matrix is the selection of the appropriate eigenvectors. We thus propose an approach based on analysis of the adjacency matrix spectrum and eigenvector pairwise correlations. Formulated rules and heuristics allow choosing the right eigenvectors representing clusters, i.e., automatically establishing the number of groups. The algorithm requires only one parameter-the number of nearest neighbors. Unlike many other spectral methods, our solution does not need an additional clustering algorithm for final partitioning. We evaluate the proposed approach using real-world datasets of different sizes. Its performance is competitive to other both standard and new solutions, which require the number of clusters to be given as an input parameter.

Graph convolutional networks (GCNs), which extend convolutional neural networks (CNNs) to non-Euclidean structures, have been utilized to promote skeleton-based human action recognition research and have made substantial progress in doing so. However, there are still some challenges in the construction of recognition models based on GCNs. In this paper, we propose an enhanced adjacency matrix-based graph convolutional network with a combinatorial attention mechanism (CA-EAMGCN) for skeleton-based action recognition. Firstly, an enhanced adjacency matrix is constructed to expand the model’s perceptive field of global node features. Secondly, a feature selection fusion module (FSFM) is designed to provide an optimal fusion ratio for multiple input features of the model. Finally, a combinatorial attention mechanism is devised. Specifically, our spatial-temporal (ST) attention module and limb attention module (LAM) are integrated into a multi-input branch and a mainstream network of the proposed model, respectively. Extensive experiments on three large-scale datasets, namely the NTU RGB+D 60, NTU RGB+D 120 and UAV-Human datasets, show that the proposed model takes into account both requirements of light weight and recognition accuracy. This demonstrates the effectiveness of our method.

In the creative design of mechanical devices，the isomorphic kinematic chains should be eliminated to reduce the mechanism scheme for subsequent design and improve the design efficiency of mechanical device. A new method for isomorphism recognition of kinematic chains is proposed based on the Hamming matrix. Firstly，the Hamming matrix of kinematic chains is educed from the link adjacency matrix，then the square matrix of Hamming matrix and the cubic matrix of link adjacency matrix are integrable to obtain the product matrix of kinematic chains. Secondly，the elements of each row in the product matrix are ordered in descending to get the row sequences of the product matrix. Finally，the isomorphism recognition code (IRC) of the kinematic chain is obtained by the sum of the product of the element in the row sequence with the defined topological factor. The isomorphism recognition code does not change with the link labels，so if the isomorphism recognition codes of the kinematic chains are the same，they are isomorphic，otherwise they are not. The effectiveness of this method is proved by a large number of examples. Because of its simplicity，efficiency and convenience for computer execution，it can be considered as a new option for isomorphism screening.

Graph coloring is the assignment of one color to each vertex of a graph so that two adjacent vertices are not of the same color. The graph coloring problem (GCP) is a matter of combinatorial optimization, and the goal of GCP is determining the chromatic number (G). Since GCP is an NP-hard problem, then in this paper, we propose a new approximated algorithm for finding the coloring number (it is an approximation of chromatic number) by using a graph adjacency matrix to colorize or separate a graph. To prove the correctness of the proposed algorithm, we implement it in MATLAB software, and for analysis in terms of solution and execution time, we compare our algorithm with some of the best existing algorithms that are already implemented in MATLAB software, and we present the results in tables of various graphs. Several available algorithms used the largest degree selection strategy, while our proposed algorithm uses the graph adjacency matrix to select the vertex that has the smallest degree for coloring. We provide some examples to compare the performance of our algorithm to other available methods. We make use of the Dolan-Moré performance profiles to assess the performance of the numerical algorithms, and demonstrate the efficiency of our proposed approach in comparison with some existing methods. [ABSTRACT FROM AUTHOR]

Different from other computer vision tasks, action recognition needs to process larger-scale video data. How to extract and analyze the effective parts from a huge amount of video information is the main difficulty of action recognition technology. In recent years, due to the outstanding performance of Graph Convolutional Networks (GCN) in many fields, a new solution to the action recognition algorithm has emerged. However, in current GCN models, the constant physical adjacency matrix makes it difficult to mine synergistic relationships between key points that are not directly connected in physical space. Additionally, a simple time connection of skeleton data from different frames makes each frame in the video contribute equally to the recognition results, which increases the difficulty of distinguishing action stages. In this paper, the information extraction ability of the model has been optimized in the space domain and time domain, respectively. In the space domain, an Adjacency Matrix Generation (AMG) module, which can pre-analyze node sets and generate an adaptive adjacency matrix, has been proposed. The adaptive adjacency matrix can help the graph convolution model to extract the synergistic information between the key points that are crucial for recognition. In the time domain, the Time Domain Attention (TDA) mechanism has been designed to calculate the time-domain weight vector through double pooling channels and complete the weights of key point sequences. Furthermore, performance of the improved TDA-AMG-GCN modules has been verified on the NTU-RGB+D dataset. Its detection accuracy at the CS and CV divisions reached 84.5% and 89.8%, respectively, with an average level higher than other commonly used detection methods at present. [ABSTRACT FROM AUTHOR]

Graph convolutional networks (GCNs), which extend convolutional neural networks (CNNs) to non-Euclidean structures, have been utilized to promote skeleton-based human action recognition research and have made substantial progress in doing so. However, there are still some challenges in the construction of recognition models based on GCNs. In this paper, we propose an enhanced adjacency matrix-based graph convolutional network with a combinatorial attention mechanism (CA-EAMGCN) for skeleton-based action recognition. Firstly, an enhanced adjacency matrix is constructed to expand the model's perceptive field of global node features. Secondly, a feature selection fusion module (FSFM) is designed to provide an optimal fusion ratio for multiple input features of the model. Finally, a combinatorial attention mechanism is devised. Specifically, our spatial-temporal (ST) attention module and limb attention module (LAM) are integrated into a multi-input branch and a mainstream network of the proposed model, respectively. Extensive experiments on three large-scale datasets, namely the NTU RGB+D 60, NTU RGB+D 120 and UAV-Human datasets, show that the proposed model takes into account both requirements of light weight and recognition accuracy. This demonstrates the effectiveness of our method. [ABSTRACT FROM AUTHOR]

Modeling complex spatial and temporal dependencies in multivariate time series data is crucial for traffic forecasting. Graph convolutional networks have proved to be effective in predicting multivariate time series. Although a predefined graph structure can help the model converge to good results quickly, it also limits the further improvement of the model due to its stationary state. In addition, current methods may not converge on some datasets due to the graph structure of these datasets being difficult to learn. Motivated by this, we propose a novel model named Dynamic Correlation Graph Convolutional Network (DCGCN) in this paper. The model can construct adjacency matrices from input data using a correlation coefficient; thus, dynamic correlation graph convolution is used for capturing spatial dependencies. Meanwhile, gated temporal convolution is used for modeling temporal dependencies. Finally, we performed extensive experiments to evaluate the performance of our proposed method against ten existing well-recognized baseline methods using two original and four public datasets. [ABSTRACT FROM AUTHOR]

Stable isotope based metabolic flux analysis is currently the unique methodology that allows the experimental study of the integrated responses of metabolic networks. This method primarily relies on isotope labeling and modeling, which could be a challenge in both experimental and computational biology. In particular, the algorithm implementation for isotope simulation is a critical step, limiting extensive usage of this powerful approach. Here, we introduce EMUlator a Python-based isotope simulator which is developed on Elementary Metabolite Unit (EMU) algorithm, an efficient and powerful algorithm for isotope modeling. We propose a novel adjacency matrix method to implement EMU modeling and exemplify it stepwise. This method is intuitively straightforward and can be conveniently mastered for various customized purposes. We apply this arithmetic pipeline to understand the phosphoketolase flux in the metabolic network of an industrial microbe Clostridium acetobutylicum. The resulting design enables a high-throughput and non-invasive approach for estimating phosphoketolase flux in vivo. Our computational insights allow the systematic design and prediction of isotope-based metabolic models and yield a comprehensive understanding of their limitations and potentials.

The research on node importance identification for temporal networks has attracted much attention. In this work, combined with the multi-layer coupled network analysis method, an optimized supra-adjacency matrix (OSAM) modeling method was proposed. In the process of constructing an optimized super adjacency matrix, the intra-layer relationship matrixes were improved by introducing the edge weight. The inter-layer relationship matrixes were formed by improved similarly and the inter-layer relationship is directional by using the characteristics of directed graphs. The model established by the OSAM method accurately expresses the structure of the temporal network and considers the influence of intra- and inter-layer relationships on the importance of nodes. In addition, an index was calculated by the average of the sum of the eigenvector centrality indices for a node in each layer and the node importance sorted list was obtained from this index to express the global importance of nodes in temporal networks. The experimental results on three real temporal network datasets Enron, Emaildept3, and Workspace showed that compared with the SAM and the SSAM methods, the OSAM method has a faster message propagation rate and larger message coverage and better SIR and NDCG@10 indicators.

Accurate forecasting of taxi demand has facilitated the rational allocation of urban public transport resources, reduced congestion in urban transport networks, and shortened passenger waiting time. However, virtual station discovery and modelling of the demand when forecasting through graph convolutional neural networks remains challenging. In this study, the virtual station discovery problem was addressed by using a two-stage clustering approach, which considers the geographical and load characteristics of taxi demand. Furthermore, a fusion model combining non-negative matrix decomposition and a graph convolutional neural network was proposed in order to extract the features of the nodes for dimension reduction and adaptive adjacency matrix computation. By the construction of a local processing structure, further extraction of the local characteristics of the demand was achieved. The experimental results show that the method in this study outperforms state-of-the-art methods in terms of the root mean square error and average absolute value error. Therefore, the model proposed in this study is able to achieve accurate forecasting of taxi demand. [ABSTRACT FROM AUTHOR]

Background: Post-translational modification (PTM) is a biological process that is associated with the modification of proteome, which results in the alteration of normal cell biology and pathogenesis. There have been numerous PTM reports in recent years, out of which, lysine phosphoglycerylation has emerged as one of the recent developments. The traditional methods of identifying phosphoglycerylated residues, which are experimental procedures such as mass spectrometry, have shown to be time-consuming and cost-inefficient, despite the abundance of proteins being sequenced in this post-genomic era. Due to these drawbacks, computational techniques are being sought to establish an effective identification system of phosphoglycerylated lysine residues. The development of a predictor for phosphoglycerylation prediction is not a first, but it is necessary as the latest predictor falls short in adequately detecting phosphoglycerylated and non-phosphoglycerylated lysine residues. Results: In this work, we introduce a new predictor named RAM-PGK, which uses sequence-based information relating to amino acid residues to predict phosphoglycerylated and non-phosphoglycerylated sites. A benchmark dataset was employed for this purpose, which contained experimentally identified phosphoglycerylated and non-phosphoglycerylated lysine residues. From the dataset, we extracted the residue adjacency matrix pertaining to each lysine residue in the protein sequences and converted them into feature vectors, which is used to build the phosphoglycerylation predictor. Conclusion: RAM-PGK, which is based on sequential features and support vector machine classifiers, has shown a noteworthy improvement in terms of performance in comparison to some of the recent prediction methods. The performance metrics of the RAM-PGK predictor are: 0.5741 sensitivity, 0.6436 specificity, 0.0531 precision, 0.6414 accuracy, and 0.0824 Mathews correlation coefficient.

In order to make it convenient for computer automatic synthesize,the automatic type synthesis of planar kinematic chains with modified Assur-group adjacency matrix is proposed. First of all,aiming at the known amount of the components,the active ones and the Assur-group,the diagonal elements with the different combination modes is solved according to the Assur-group theory. Then the synthesis method and concrete process is summarized and the selected Assur-group adjacency matrix is defined. The kinematic chains are subdivided in terms of 3 conditions of pole number,active pole and Assur-group type,meanwhile the isomorphism is estimated. As a conclusion,the method has better regularity,high efficiency and is beneficial to eliminate the rigid chains and reduce the calculation workload of isomorphism identification. Especially,the method can be applied to the automatic type synthesis for the planar mechanism kinematic chains with multiple links and multiple degrees of freedom. In addition,the success is achieved in the application on the type synthesis for the planar closed kinematic chains with 12 links and 12-below-links. Finally,the type synthesis method is demonstrated with the example of kinematic chains with 6 links and single degree of freedom.

The isomorphism identification of structural type is a vital problem now. For dealing with the isomorphism generated in synthesis of planar configuration based on the synthesis method of Assur- group adjacency matrix,a methodology of Assur- group adjacency matrix isomorphism identification is proposed. First of all,according to the diagonal elements is derived by the amount of Assur- group and active number,the diagonal isomorphism identification is obtained. Then,the condition is classified into three kinds,first is sequence isomorphism when Assur- group is equipped,second is symmetrical configuration isomorphism after adding Assur- group and the last one is discovered in matrix synthesis,which would be recognized and deleted by this method. Finally,the methodology proposed is able to be achieved by computer,easy to control and takes high efficiency in isomorphism identification.