Yi Yan

Yi Yan, Radwa Adel, Ercan Engin Kuruoglu

In this paper, we introduce an adaptive graph normalized least mean pth power (GNLMP) algorithm for graph signal processing (GSP) that utilizes GSP techniques, including bandlimited filtering and node sampling, to estimate sampled graph signals under impulsive noise. Different from least-squares-based algorithms, such as the adaptive GSP Least Mean Squares (GLMS) algorithm and the normalized GLMS (GNLMS) algorithm, the GNLMP algorithm has the ability to reconstruct a graph signal that is corrupted by non-Gaussian noise with heavy-tailed characteristics. Compared to the recently introduced adaptive GSP least mean pth power (GLMP) algorithm, the GNLMP algorithm reduces the number of iterations to converge to a steady graph signal. The convergence condition of the GNLMP algorithm is derived, and the ability of the GNLMP algorithm to process multidimensional time-varying graph signals with multiple features is demonstrated as well. Simulations show the performance of the GNLMP algorithm in estimating steady-state and time-varying graph signals is faster than GLMP and more robust in comparison to GLMS and GNLMS.

Yi Yan, Ercan Engin Kuruoglu

Spatio-temporal estimation of signals on graph edges is challenging because most conventional Graph Signal Processing techniques are defined on the graph nodes. Leveraging the Line Graph transform, the Line Graph Least Mean Square (LGLMS) algorithm is proposed to conduct adaptive estimation of time-varying edge signals by projecting the edge signals from edge space to node space. LGLMS is an adaptive algorithm analogous to the classical LMS algorithm but applied to graph edges. Unlike edge-specific methods, LGLMS retains all GSP concepts and techniques originally designed for graph nodes, without the need for redefinition on the edges. Experimenting with transportation graphs and meteorological graphs, with the signal observations having noisy and missing values, we confirmed that LGLMS is suitable for the online prediction of time-varying edge signals.

Yi Yan, Ercan E. Kuruoglu

Graph Neural Networks have a limitation of solely processing features on graph nodes, neglecting data on high-dimensional structures such as edges and triangles. Simplicial Convolutional Neural Networks (SCNN) represent higher-order structures using simplicial complexes to break this limitation albeit still lacking time efficiency. In this paper, we propose a novel neural network architecture on simplicial complexes named Binarized Simplicial Convolutional Neural Networks (Bi-SCNN) based on the combination of simplicial convolution with a binary-sign forward propagation strategy. The usage of the Hodge Laplacian on a binary-sign forward propagation enables Bi-SCNN to efficiently and effectively represent simplicial features that have higher-order structures than traditional graph node representations. Compared to the previous Simplicial Convolutional Neural Networks, the reduced model complexity of Bi-SCNN shortens the execution time without sacrificing the prediction performance and is less prone to the over-smoothing effect. Experimenting with real-world citation and ocean-drifter data confirmed that our proposed Bi-SCNN is efficient and accurate.

Yi Yan, Changran Peng, Ercan Engin Kuruoglu

This paper proposes Graph Signal Adaptive Message Passing (GSAMP), a novel message passing method that simultaneously conducts online prediction, missing data imputation, and noise removal on time-varying graph signals. Unlike conventional Graph Signal Processing methods that apply the same filter to the entire graph, the spatiotemporal updates of GSAMP employ a distinct approach that utilizes localized computations at each node. This update is based on an adaptive solution obtained from an optimization problem designed to minimize the discrepancy between observed and estimated values. GSAMP effectively processes real-world, time-varying graph signals under Gaussian and impulsive noise conditions.

Yi Yan, Dayu Qin, Ercan Engin Kuruoglu

This work introduces the LLM Online Spatial-temporal Reconstruction (LLM-OSR) framework, which integrates Graph Signal Processing (GSP) and Large Language Models (LLMs) for online spatial-temporal signal reconstruction. The LLM-OSR utilizes a GSP-based spatial-temporal signal handler to enhance graph signals and employs LLMs to predict missing values based on spatiotemporal patterns. The performance of LLM-OSR is evaluated on traffic and meteorological datasets under varying Gaussian noise levels. Experimental results demonstrate that utilizing GPT-4-o mini within the LLM-OSR is accurate and robust under Gaussian noise conditions. The limitations are discussed along with future research insights, emphasizing the potential of combining GSP techniques with LLMs for solving spatiotemporal prediction tasks.

Dayu Qin, Yi Yan, Ercan Engin Kuruoglu

In this paper, we propose a novel framework that leverages large language models (LLMs) for predicting missing values in time-varying graph signals by exploiting spatial and temporal smoothness. We leverage the power of LLM to achieve a message-passing scheme. For each missing node, its neighbors and previous estimates are fed into and processed by LLM to infer the missing observations. Tested on the task of the online prediction of wind-speed graph signals, our model outperforms online graph filtering algorithms in terms of accuracy, demonstrating the potential of LLMs in effectively addressing partially observed signals in graphs.

Yi Yan, Changran Peng, Ercan Engin Kuruoglu

The online prediction of multivariate signals, existing simultaneously in space and time, from noisy partial observations is a fundamental task in numerous applications. We propose an efficient Neural Network architecture for the online estimation of time-varying graph signals named the Adaptive Least Mean Squares Graph Neural Networks (LMS-GNN). LMS-GNN aims to capture the time variation and bridge the cross-space-time interactions under the condition that signals are corrupted by noise and missing values. The LMS-GNN is a combination of adaptive graph filters and Graph Neural Networks (GNN). At each time step, the forward propagation of LMS-GNN is similar to adaptive graph filters where the output is based on the error between the observation and the prediction similar to GNN. The filter coefficients are updated via backpropagation as in GNN. Experimenting on real-world temperature data reveals that our LMS-GNN achieves more accurate online predictions compared to graph-based methods like adaptive graph filters and graph convolutional neural networks.

Guoyu Zhou, Jing Zhang, Yi Yan et al.

Semantic segmentation of urban remote sensing images (URSIs) is crucial for applications such as urban planning and environmental monitoring. However, geospatial objects often exhibit subtle texture differences and similar spatial structures, which can easily lead to semantic ambiguity and misclassification. Moreover, challenges such as irregular object shapes, blurred boundaries, and overlapping spatial distributions of semantic objects contribute to complex and diverse edge morphologies, further complicating accurate segmentation. To tackle these issues, we propose a texture-aware and edge-guided Transformer (TEFormer) that integrates texture awareness and edge-guidance mechanisms for semantic segmentation of URSIs. In the encoder, a texture-aware module (TaM) is designed to capture fine-grained texture differences between visually similar categories to enhance semantic discrimination. Then, an edge-guided tri-branch decoder (Eg3Head) is constructed to preserve local edges and details for multiscale context-awareness. Finally, an edge-guided feature fusion module (EgFFM) is to fuse contextual and detail information with edge information to realize refined semantic segmentation. Extensive experiments show that TEFormer achieves mIoU of 88.57%, 81.46%, and 53.55% on the Potsdam, Vaihingen, and LoveDA datasets, respectively, shows the effectiveness in URSI semantic segmentation.

Yi Yan, Changran Peng, Ercan E. Kuruoglu

In the presence of impulsive noise, and missing observations, accurate online prediction of time-varying graph signals poses a crucial challenge in numerous application domains. We propose the Adaptive Least Mean $p^{th}$ Power Graph Neural Networks (LMP-GNN), a universal framework combining adaptive filter and graph neural network for online graph signal estimation. LMP-GNN retains the advantage of adaptive filtering in handling noise and missing observations as well as the online update capability. The incorporated graph neural network within the LMP-GNN can train and update filter parameters online instead of predefined filter parameters in previous methods, outputting more accurate prediction results. The adaptive update scheme of the LMP-GNN follows the solution of a $l_p$-norm optimization, rooting to the minimum dispersion criterion, and yields robust estimation results for time-varying graph signals under impulsive noise. A special case of LMP-GNN named the Sign-GNN is also provided and analyzed, Experiment results on two real-world datasets of temperature graph and traffic graph under four different noise distributions prove the effectiveness and robustness of our proposed LMP-GNN.