In recent years, distributed estimation of graph Laplacian matrices for smooth graph signals has received much attention. Traditional methods for estimating the graph Laplacian matrices usually estimate the global parameters in a centralized manner, which is computationally intensive and hard to apply in large-scale networks. In this paper, in order to reduce the computational complexity and meanwhile maintain the estimation accuracy, we propose a distributed graph Laplacian matrix estimation method called the distributed combinatorial graph Laplacian estimation (DCGL). In our method, a local parameter estimation problem is first formulated for each vertex by maximizing the marginal likelihood of the data collected from the neighborhood of the vertex. Then, by discussing the connectivity and Laplacian property of the marginal precision matrix, the Laplacian and structural constraints are added to each local estimation problem to resolve the non-convexity between the local and global estimates. Finally, through a simple and single message-passing rule, the global graph Laplacian matrix is obtained by extracting, combining, and symmetrizing the locally estimated parameters. Experiments on synthetic and real datasets demonstrate that the proposed distributed estimator is asymptotically consistent in the classical regime while having advantages in the high-dimensional regime.

3D object classification is an important task in computer vision. In order to explore the high-order and multi-modal correlations among 3D data, we propose an adaptive multi-hypergraph convolutional networks (AMHCN) framework to enhance 3D object classification performance. The proposed network improves the current hypergraph neural networks in two aspects. Firstly, existing networks rely on hyperedge constrained neighborhoods for feature aggregation, which may introduce noise or ignore positive information outside the hyperedges. To this end, we develop the partially absorbing random walks (PARW) to hypergraph for capturing optimal vertex neighborhoods from hypergraph globally. Then, based on the PARW on hypergraph, we design a new hypergraph convolution operator to learn deep embeddings from the optimized high-order correlation, which enables effective information propagation among the most relevant vertices. Secondly, concerning the multi-modal representations in practice, the current multi-modal hypergraph learning models either treat all modalities equally or introduce abundant parameters to learn weights of different modalities. To overcome these shortcomings, we propose a simple but effective dynamic weighting strategy for combining multi-modal representations, in which the importance of each modality can be adjusted adaptively by the loss function. We apply the proposed model to 3D object classification, and the experimental results on two 3D benchmark datasets demonstrate that our method outperforms the state-of-the-art methods, testifying to the effectiveness of both our convolution method and multi-modality fusion strategy.

Recently, hypergraph learning has shown great potential in a variety of classification tasks. However, existing hypergraph neural networks lack flexibility in modeling and extracting high-order relationships among data. To solve this problem, we propose a novel framework called hypergraph wavelet neural networks (HGWNN) to explore the high-order correlation in 3D data. Firstly, considering the non-uniformity of most data sets in the real world, we propose a “data-driven” hypergraph construction scheme, which is more efficient than some commonly used hypergraph construction methods. Secondly, in order to efficiently learn deep embeddings from the constructed hypergraph, we propose a hypergraph wavelet convolution operator. It enables efficient information aggregation by fully exploiting the localization property of wavelets. This convolution operator is suitable for both non-uniform and uniform hypergraphs. Finally, we design a new hypergraph regularizer based on the sparse prior of wavelet coefficients to promote local smoothness and avoid network overfitting. We have conducted experiments on object classification tasks on two 3D benchmark datasets: the National Taiwan University (NTU) 3D model dataset and the ModelNet40 dataset. Experimental results demonstrate the effectiveness of the proposed method compared with the state-of-the-art methods.

In this work, we consider a multiuser communication system in fading channels where the transmitter is supplied by hybrid energy sources including power grid and various renewable sources. Specially, the energy harvested from various renewable sources is stored in a limited capacity buffer, and the joint energy incoming is time-varying and possibly unpredictable. In addition, data arrives randomly to the transmitter and queues according to the individual receivers, the wireless channels fluctuate randomly due to fading. Our goal is, under this condition to develop a dynamic power allocation algorithm so as to minimize the time average amount of energy consumed from the power grid over an infinite horizon, subjecting to all data queues stability. The issue is formulated as a stochastic optimization problem and solved by Lyapunov optimization technique which does not require the statistical probabilities of energy harvesting process, data arrivals process and channel state. Simulation results demonstrate that our proposed algorithm provides obviously better performance than other two simple greedy algorithms, meanwhile the algorithm gives a guarantee that the maximum delay of all data queues cannot exceed a given value.