In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and established, the field of dynamic network embedding is comparatively in its infancy. We propose that a wide class of established static network embedding methods can be used to produce interpretable and powerful dynamic network embeddings when they are applied to the dilated unfolded adjacency matrix. We provide a theoretical guarantee that, regardless of embedding dimension, these unfolded methods will produce stable embeddings, meaning that nodes with identical latent behaviour will be exchangeable, regardless of their position in time or space. We additionally define a hypothesis testing framework which can be used to evaluate the quality of a dynamic network embedding by testing for planted structure in simulated networks. Using this, we demonstrate that, even in trivial cases, unstable methods are often either conservative or encode incorrect structure. In contrast, we demonstrate that our suite of stable unfolded methods are not only more interpretable but also more powerful in comparison to their unstable counterparts.
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Corn Yield Prediction Model with Deep Neural Networks for Smallholder Farmer Decision Support System
Given the nonlinearity of the interaction between weather and soil variables, a novel deep neural network regressor (DNNR) was carefully designed with considerations to the depth, number of neurons of the hidden layers, and the hyperparameters with their optimizations. Additionally, a new metric, the average of absolute root squared error (ARSE) was proposed to address the shortcomings of root mean square error (RMSE) and mean absolute error (MAE) while combining their strengths. Using the ARSE metric, the random forest regressor (RFR) and the extreme gradient boosting regressor (XGBR), were compared with DNNR. The RFR and XGBR achieved yield errors of 0.0000294 t/ha, and 0.000792 t/ha, respectively, compared to the DNNR(s) which achieved 0.0146 t/ha and 0.0209 t/ha, respectively. All errors were impressively small. However, with changes to the explanatory variables to ensure generalizability to unforeseen data, DNNR(s) performed best. The unforeseen data, different from unseen data, is coined to represent sudden and unexplainable change to weather and soil variables due to climate change. Further analysis reveals that a strong interaction does exist between weather and soil variables. Using precipitation and silt, which are strong-negatively and strong-positively correlated with yield, respectively, yield was observed to increase when precipitation was reduced and silt increased, and vice-versa.
Network dynamic (e.g., traffic burst in data center networks and channel fading in cellular WiFi networks) has a great impact on the performance of communication networks (e.g., throughput, capacity, delay, and jitter). This article proposes a unified prediction-based method to handle the dynamic of various network systems. From the view of graph deep learning, I generally formulate the dynamic prediction of networks as a temporal link prediction task and analyze the possible challenges of the prediction of weighted networks, where link weights have the wide-value-range and sparsity issues. Inspired by the high-resolution video frame prediction with generative adversarial network (GAN), I try to adopt adversarial learning to generate high-quality predicted snapshots for network dynamic, which is expected to support the precise and fine-grained network control. A novel high-quality temporal link prediction (HQ-TLP) model with GAN is then developed to illustrate the potential of my basic idea. Extensive experiments for various application scenarios further demonstrate the powerful capability of HQ-TLP.
In this paper, we study underlay device-to-device (D2D) communication systems empowered by a reconfigurable intelligent surface (RIS) for cognitive cellular networks. Considering Rayleigh fading channels and the general case where there exist both the direct and RIS-enabled D2D channels, the outage probability (OP) of the D2D communication link is presented in closed-form. Next, for the considered RIS-empowered underlaid D2D system, we frame an OP minimization problem. We target the joint optimization of the transmit power at the D2D source and the RIS placement, under constraints on the transmit power at the D2D source and on the limited interference imposed on the cellular user for two RIS deployment topologies. Due to the coupled optimization variables, the formulated optimization problem is extremely intractable. We propose an equivalent transformation which we are able to solve analytically. In the transformed problem, an expression for the average value of the signal-to-interference-noise ratio (SINR) at the D2D receiver is derived in closed-form. Our theoretical derivations are corroborated through simulation results, and various system design insights are deduced. It is indicatively showcased that the proposed RIS-empowered underlaid D2D system design outperforms the benchmark semi-adaptive optimal power and optimal distance schemes, offering $44\%$ and $20\%$ performance improvement, respectively.
With the aim of boosting the security of the conventional directional modulation (DM) network, a secure DM network assisted by intelligent reflecting surface (IRS) is investigated in this paper. To maximize the security rate (SR), we jointly optimize the power allocation (PA) factor, confidential message (CM) beamforming, artificial noise (AN) beamforming, and IRS reflected beamforming. To tackle the formulated problem, a maximizing SR with high-performance (Max-SR-HP) scheme is proposed, where the PA factor, CM beamforming, AN beamforming, and IRS phase shift matrix are derived by the derivative operation, generalized Rayleigh-Rize, generalized power iteration, and semidefinite relaxation criteria, respectively. Given that the high complexity of the above scheme, a maximizing SR with low-complexity (Max-SR-LC) scheme is proposed, which employs the generalized leakage and successive convex approximation algorithms to derive the variables. Simulation results show that both the proposed schemes can significantly boost the SR performance, and are better than the equal PA, no IRS and random phase shift IRS schemes.
Longitudinal network consists of a sequence of temporal edges among multiple nodes, where the temporal edges are observed in real time. It has become ubiquitous with the rise of online social platform and e-commerce, but largely under-investigated in literature. In this paper, we propose an efficient estimation framework for longitudinal network, leveraging strengths of adaptive network merging, tensor decomposition and point process. It merges neighboring sparse networks so as to enlarge the number of observed edges and reduce estimation variance, whereas the estimation bias introduced by network merging is controlled by exploiting local temporal structures for adaptive network neighborhood. A projected gradient descent algorithm is proposed to facilitate estimation, where the upper bound of the estimation error in each iteration is established. A thorough analysis is conducted to quantify the asymptotic behavior of the proposed method, which shows that it can significantly reduce the estimation error and also provides guideline for network merging under various scenarios. We further demonstrate the advantage of the proposed method through extensive numerical experiments on synthetic datasets and a militarized interstate dispute dataset.
In this paper, we provide the first convergence guarantee for the factorization approach. Specifically, to avoid the scaling ambiguity and to facilitate theoretical analysis, we optimize over the so-called left-orthogonal TT format which enforces orthonormality among most of the factors. To ensure the orthonormal structure, we utilize the Riemannian gradient descent (RGD) for optimizing those factors over the Stiefel manifold. We first delve into the TT factorization problem and establish the local linear convergence of RGD. Notably, the rate of convergence only experiences a linear decline as the tensor order increases. We then study the sensing problem that aims to recover a TT format tensor from linear measurements. Assuming the sensing operator satisfies the restricted isometry property (RIP), we show that with a proper initialization, which could be obtained through spectral initialization, RGD also converges to the ground-truth tensor at a linear rate. Furthermore, we expand our analysis to encompass scenarios involving Gaussian noise in the measurements. We prove that RGD can reliably recover the ground truth at a linear rate, with the recovery error exhibiting only polynomial growth in relation to the tensor order. We conduct various experiments to validate our theoretical findings.
We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed line energy probability density function is derived from the Fokker--Planck equation of the full-order continuous Markov process. Our method consists of estimates produced by numerically integrating this reduced equation. Numerical experiments for scalar- and vector-valued energy functions are conducted using the classical multimachine model under spatiotemporally correlated noise perturbation. The method demonstrates a more sample-efficient approach for computing probabilities of tail events when compared with kernel density estimation. Moreover, it produces vastly more accurate estimates of joint event occurrence when compared with independent models.
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.
A large number of real-world graphs or networks are inherently heterogeneous, involving a diversity of node types and relation types. Heterogeneous graph embedding is to embed rich structural and semantic information of a heterogeneous graph into low-dimensional node representations. Existing models usually define multiple metapaths in a heterogeneous graph to capture the composite relations and guide neighbor selection. However, these models either omit node content features, discard intermediate nodes along the metapath, or only consider one metapath. To address these three limitations, we propose a new model named Metapath Aggregated Graph Neural Network (MAGNN) to boost the final performance. Specifically, MAGNN employs three major components, i.e., the node content transformation to encapsulate input node attributes, the intra-metapath aggregation to incorporate intermediate semantic nodes, and the inter-metapath aggregation to combine messages from multiple metapaths. Extensive experiments on three real-world heterogeneous graph datasets for node classification, node clustering, and link prediction show that MAGNN achieves more accurate prediction results than state-of-the-art baselines.
In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.
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