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The prevalence of multi-dimensional (m-D) graph signals in various real-world applications, such as digital images and data with spatial and temporal dimensions, highlights their significance. However, efficiently sampling and reconstructing these m-D graph signals remains a significant challenge in the field of graph signal processing. In this paper, we study the generalized sampling framework of m-D graph signals based on prior knowledge. First, we consider the subspace priors of m-D graph signals, assuming that the signals are located in the periodic m-D graph spectral subspace. We design the reconstruction scheme through the subspace prior information. Then, we propose a generalized sampling framework for m-D graph signals based on smoothness prior information with lower constraints. It is still possible to recover the original m-D graph signal when the space where the m-D graph signal is located is unknown. In the above framework, sampling and reconstruction can be implemented efficiently, and there is no bandwidth limitation for the m-D graph signals. Finally, several experiments are performed to numerically validate the effectiveness of the proposed sampling framework. • We develop a sampling framework for m-D graph signals based on a subspace prior. • When the space is unknown, the original m-D graph signal can be reconstructed. • Our m-D graph signal sampling method is scalable. [ABSTRACT FROM AUTHOR]

It is very significant to learn graph representation by using only the network topology information in many application scenarios, where attributes of nodes are not available or not easy to obtain. Although existing approaches have achieved impressive performance, they cannot deterministically involve important nodes related to the current node in the representation learning process, leading to a lack of robustness. To address this problem, we propose a novel symmetric cumulative sampling strategy for unsupervised graph representation learning via multi-step propagation and aggregation sampling, named MPMA. According to generated hierarchical transition probabilities, MPMA is able to select crucial nodes and construct pyramidal node subsets from both propagation and aggregation perspectives. Based on the constructed node subsets, an efficient algorithm is employed to search the shortest paths between the current node and each important node to preserve sufficient interaction of nodes. Extensive experiments on diverse application tasks verify the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Graph sampling is a challenging problem in network analysis due to the complex structures of networks. Currently, a series of graph sampling algorithms based on random walks achieve good results in graph sampling tasks. However, the existing methods often reduce the conductance of graphs, causing the sampler to stay in the same node for a long time. This results in undersampling. In this paper, we propose a novel Weighted Jump Random Walk (WJRW) algorithm to generate representative samples. We design a parameter in the WJRW algorithm that can adjust the proportions of random walk and random jump in every step. According to the issue of repeated sample nodes in the Generalized Maximum Degree (GMD) method and the problem of large deviations in the Simple Random Walk (SRW), WJRW addresses the weaknesses of the GMD method and enhances the diffusion of a random walker on graphs, leading to a more representative sample. Then, WJRW addresses the issue of large deviations in SRW and enhances the efficiency of the unbiased estimator. By generating smoother stationary distributions. Numerical experiments with extensive real-world networks verify that our method achieves higher accuracy than classical and state-of-the-art methods in estimating distribution estimation. [ABSTRACT FROM AUTHOR]

Frequent pattern mining (FPM), whose goal is to identify patterns with appearance frequencies above a specified support threshold on a large graph, has attracted increasing attention owing to its diverse applications. The task suffers from an issue of support setting, as an inappropriate support threshold may lead to either extremely high computational cost along with a huge pattern set or very few patterns caused by excessive pruning. Thus, supports estimation is crucial for FPM, since an appropriate support threshold enables users to discover a limited number of patterns within affordable computational resources. In light of this, we investigate the problem of supports estimation under the constraint of pattern number B and propose a comprehensive approach to the issue. Our approach leverages a neural network to predict the support θ B that corresponds to the B -th pattern on a graph G. To train the prediction model, we first present a sampling algorithm that leverages typical motifs to produce sampled graphs of G under different sampling ratios. Owing to the typical structures brought about by motifs, the sampled graphs are embedded supports of the top-ranked patterns in proportion to the sampling ratios. We next develop techniques to efficiently infer the support θ B of the B -th pattern on each sampled graph and introduce a method to encode (sampled) graphs with θ B and other typical features, thereby forming the training data. Extensive experimental studies on real-life and synthetic graphs demonstrate the superiority of our approach, compared to other baselines. • We introduce a motifs-based graph sampling algorithm that reserves salient features. • We develop a support-threshold-free mining algorithm to identify top-B patterns. • We built a neural network model to perform support estimation. [ABSTRACT FROM AUTHOR]

In modern dairy farms, accurate and reliable identification of each individual cow is of great significance for precision livestock farming. Individual cow identification is the basis for applications such as disease detection, automatic behaviour analysis, intelligent milking, and individual counting and is crucial for improving the welfare and breeding efficiency of dairy cows. Computer vision-based method is a low-cost, non-contact, automatic, and efficient way. To improve the accuracy and efficiency of cow recognition in different large-scale dairy farms, we proposed a BottleNet Transformer (BoTNet) model based on Graph Sampling and Counterfactual Attention Learning for cow surveillance videos. First, we replace the 3 × 3 spatial convolution with Multi-Head Attention in the final three bottleneck blocks of the ResNet. The BoT block module combines attention mechanisms and residual connection to enhance the global representation of cow images, which in turn better captures the features of the cow's back pattern region and ignores the influence of irrelevant information, such as the background of the dairy barn. Subsequently, counterfactual learning measures the quality of attention by comparing the difference between the generated output and the true label. The difference can be used to enhance the causal relationship between prediction results and cow feature attention, allowing the model to obtain more comprehensive cow appearance features. Finally, we added a Graph Sampling module before the feature extraction phase to produce small batches of samples for training. The GS sampler improves the learning efficiency while reducing the memory and computation consumption compared with the usual adopted PK sampling. We conducted comparison experiments on the public dataset Dataset1, and the experimental results reveal that the Rank-1, Rank-5, and mAP values of this study's method are 4%, 3.2%, and 5.3% higher than the optimal results, respectively, when compared with the existing state-of-the-art methods for animal individual recognition. In particular, we construct a challenging dataset by intercepting individual cow images from videos in the public dataset of farms. Experimental results indicate that the proposed method has better generalization performance. • We propose a cost-efficient cow individual recognition method for large dairy farms. • Bottleneck Transformer is used to capture the global and Local features of cow backs. • Counterfactual learning pays more attention to cow backs and ignores backgrounds. • Graph Sampling is adopted to reduce memory and computation during training. [ABSTRACT FROM AUTHOR]

The graph fractional Fourier transform (GFRFT) has been applied to graph signal processing and has become an important tool in graph signal processing. However, most of the graph signals are usually non-bandlimited in the GFRFT domain. How to efficiently sampling and reconstructing these graph signals is a key challenge in the field of graph signal processing. In this paper, we propose a generalized sampling framework for graph signals based on the prior information in the GFRFT domain. In this framework, sampling and reconstruction can be efficiently implemented. Moreover, the framework is not limited by the bandwidth of the fractional Fourier domain of the graph signal. In this study, we first consider the subspace prior of the graph signal. It allows arbitrary input of the graph signal with or without bandlimited in the GFRFT domain. Then, we propose a generalized sampling framework for graph signals based on smoother prior information associated with GFRFT. When the prior space of the graph signal is unknown, the original graph signal can still be reconstructed. Finally, we compare our method with existing sampling techniques. Several experiments are performed to numerically validate the effectiveness of the proposed sampling framework. • we develop a generalized sampling framework for graph signals based on the GFRFT. • It allows arbitrary input of the graph signal with or without bandlimited in the GFRFT domain. • When the space and smoothness are unknown, the original graph signal can be reconstructed. • Our method is superior to other graph sampling schemes. [ABSTRACT FROM AUTHOR]

Providing reliable and accurate wind speed predictions for the power system ensures a stable power output. However, the high wind speed uncertainty and the complex spatial–temporal correlation between wind turbines still make wind speed prediction a significant challenge. This paper proposes a novel dynamic spatial–temporal graph network (DSTGN) to make wind speed predictions by accurately capturing the dynamic dependencies of multi-turbine on an arbitrary graph structure. DSTGN adopts an extensible and serialized structure consisting of stacked dynamic spatial–temporal blocks to model dependencies. In spatial dependency extraction, a graph generation module is used in the spatial block to produce static and dynamic spatial information. A parameterized adjacency matrix expands the spatial hypothesis space rather than being limited by the distance between turbines. In temporal dependency extraction, the multi-head attention mechanism models temporal associations of diverse time horizons. Based on publicly available wind datasets, extensive experimental results showed that the proposed model significantly improves performance. Compared to recent state-of-the-art models, MAE, RMSE and MAPE are improved over 4.57%, 4.25% and 8.31%, respectively. Furthermore, through ablation studies, we verified the benefits of each component of the proposed model, especially the positive role of graph sampling in improving performance. • A parameterized strategy makes the adjacency matrix break through traditional distance limitations. • The proposed model can handle spatial features when the adjacency matrix is unavailable. • Dynamic spatial dependencies at every time step can be tapped. • The graph sampling deals with the over-smoothing problem. • Results suggest the proposed model can produce more accurate predictions and be adaptive to different conditions. [ABSTRACT FROM AUTHOR]

Discriminative systems that can deal with graphs in input are known, however, generative or constructive approaches that can sample graphs from empirical distributions are less developed. Here we propose a Metropolis–Hastings approach that uses a novel type of graph grammar to efficiently learn proposal distributions in a data driven fashion. We report experimental results in a de-novo molecular synthesis problem where we show that the distribution of the molecules generated by the sampling procedure is accurate enough to improve a predictor's performance in a classification task. [ABSTRACT FROM AUTHOR]

• Aresent a graph sampling & aggregation scheme for solving large-scale supply chain problems. • Approach provides valid upper and lower bounds. • Approach overcome scalability bottlenecks of state-of-the-art mixed-integer solvers. We present a graph sampling and coarsening scheme (gSC) for computing lower and upper bounds for large-scale supply chain models. An edge sampling scheme is used to build a low-complexity problem that is used to finding an approximate (but feasible) solution for the original model and to compute a lower bound (for a maximization problem). This scheme is similar in spirit to the so-called sample average approximation scheme, which is widely used for the solution of stochastic programs. A graph coarsening (aggregation) scheme is used to compute an upper bound and to estimate the optimality gap of the approximate solution. The coarsening scheme uses node sampling to select a small set of support nodes that are used to guide node/edge aggregation and we show that the coarsened model provides a relaxation of the original model and a valid upper bound. We provide evidence that gSC can yield significant improvements in solution time and memory usage over state-of-the-art solvers. Specifically, we study a supply chain design model (a mixed-integer linear program) that contains over 38 million variables and show that gSC finds a solution with an optimality gap of < 0.5 % in less than 22 minutes. [ABSTRACT FROM AUTHOR]

Social networks content analysis has become more challenging over the years due to the rapidly increasing amount of data. Real social networks are omnipresent in everyday life, which makes the structure of the generated data more complex. A key task in social networks analysis is to reduce the network' s size and to produce an approximate representation that preserves the original network' s properties. This task is known as graph' s reduction and is gaining increasing attention in the scientific community. A review of literature reveals diverse methods to address this task. Some of them are based on graph coarsening and are developed to cope with the problem of communities detection. Others are part of graph sampling and are designed to reduce the graph' s size while preserving its structure, which is our purpose. In this paper, we put forth a distributed model called DGS "Distributed Graph Sampling" to generate a sample in a distributed way. The idea behind distributing our model is to cope with large scale social networks. In effect, our model is based on the MapReduce framework that allows to access simultaneously to several data segments for the calculation during the sampling strategy. The main task of our model is to use a new centrality measure based on the degree centrality to sample the graph. We evaluate the performance and the scalability of our DGS model using real world social networks. In this paper, we will compare our proposed model to four well-known sampling strategies in order to demonstrate its efficiency to preserve the original network' s structure. • We investigate the effects of graph sampling on reducing the graph's size. • We produce an approximate representation that retains the graph's structure. • Our distributed method DGS is based on the MapReduce paradigm. • DGS is able to cope with large scale social networks. • For real world social networks our model demonstrates its efficiency. [ABSTRACT FROM AUTHOR]