Variational Graph Autoencoder Research Articles

Expressway Vehicle Trajectory Prediction Based on Fusion Data of Trajectories and Maps from Vehicle Perspective

Research on vehicle trajectory prediction based on road monitoring video data often utilizes a global map as an input, disregarding the fact that drivers rely on the road structures observable from their own positions for path planning. This oversight reduces the accuracy of prediction. To address this, we propose the CVAE-VGAE model, a novel trajectory prediction approach. Initially, our method transforms global perspective map data into vehicle-centric map data, representing it through a graph structure. Subsequently, Variational Graph Auto-Encoders (VGAEs), an unsupervised learning framework tailored for graph-structured data, are employed to extract road environment features specific to each vehicle’s location from the map data. Finally, a prediction network based on the Conditional Variational Autoencoder (CVAE) structure is designed, which first predicts the driving endpoint and then fits the complete future trajectory. The proposed CVAE-VGAE model integrates a self-attention mechanism into its encoding and decoding modules to infer endpoint intent and incorporate road environment features for precise trajectory prediction. Through a series of ablation experiments, we demonstrate the efficacy of our method in enhancing vehicle trajectory prediction metrics. Furthermore, we compare our model with traditional and frontier approaches, highlighting significant improvements in prediction accuracy.

A Construction Method for a Dynamic Weighted Protein Network Using Multi-Level Embedding

The rapid development of high-throughput technology has generated a large amount of protein–protein interaction (PPI) data, which provide a large amount of data support for constructing dynamic protein–protein interaction networks (PPINs). Constructing dynamic PPINs and applying them to recognize protein complexes has become a hot research topic. Most existing methods for complex recognition cannot fully mine the information of PPINs. To address this problem, we propose a construction method of dynamic weighted protein network by multi-level embedding (DWPNMLE). It can reflect the protein network’s dynamics and the protein network’s higher-order proximity. Firstly, the protein active period is calculated to divide the protein subnetworks at different time points. Then, the connection probability is used for the proteins possessing the same time points to judge whether there is an interaction relationship between them. Then, the corresponding protein subnetworks (multiple adjacency matrices) are constructed. Secondly, the multiple feature matrices are constructed using one-hot coding with the gene ontology (GO) information. Next, the first embedding is performed using variational graph auto-encoders (VGAEs) to aggregate features efficiently, followed by the second embedding using deep attributed network embedding (DANE) to strengthen the node representations learned in the first embedding and to maintain the first-order and higher-order proximity of the original network; finally, we compute the cosine similarity to obtain the final dynamic weighted PPIN. To evaluate the effectiveness of DWPNMLE, we apply four classical protein-complex-recognition algorithms on the DWPNMLE and compare them with two other dynamic protein network construction methods. The experimental results demonstrate that DWPNMLE significantly enhances the accuracy of complex recognition with high robustness, and the algorithms’ efficiency is also within a reasonable range.

A parameterised model for link prediction using node centrality and similarity measure based on graph embedding

Link prediction is a crucial aspect of graph machine learning, with applications as diverse as disease prediction, social network recommendations, and drug discovery. It involves the prediction of potential new links between nodes within a network. Despite its importance, current models for link prediction exhibit notable limitations. Graph Convolutional Networks have shown high efficiency in link prediction across various datasets. However, they face significant challenges when applied to short-path networks and ego networks, resulting in poor performance. This issue represents a critical area of concern that our work seeks to address. This paper introduces the Node Centrality and Similarity Based Parameterised Model (NCSM), a novel method for link prediction tasks. NCSM uniquely integrates node centrality and similarity measures as edge features in a customised Graph Neural Network (GNN) layer, effectively leveraging the topological information of large networks. This model represents the first parameterised GNN-based link prediction model that considers topological information. The proposed model was evaluated on five benchmark graph datasets, each comprising thousands of nodes and edges. Experimental results highlight NCSM's superiority over existing state-of-the-art models like Graph Convolutional Networks and Variational Graph Autoencoder, as it outperforms them across various metrics and datasets. This exceptional performance can be attributed to NCSM's innovative integration of node centrality, similarity measures, and its efficient use of topological information.

Design of an Iterative Method for Enhanced Multimodal Time Series Analysis Using Graph Attention Networks, Variational Graph Autoencoders, and Transfer Learning

In the ever-evolving landscape of data analysis, the need to efficiently and accurately interpret multimodal time series data has become paramount. Traditional methods often fall short in addressing the complex dependencies and dynamics inherent in such data, limiting their effectiveness in real-world applications. This work introduces a comprehensive approach that leverages Graph Attention Networks (GATs), Variational Graph Autoencoders (VGAEs), transfer learning with pretrained transformers, and Bayesian state-space models to overcome these limitations. GATs are selected for their ability to dynamically focus on relevant modalities through attention mechanisms, thereby capturing the intricate relationships between different data modalities. This method significantly enhances the model's ability to integrate multimodal information, leading to notable improvements in classification, prediction, and anomaly detection tasks. VGAEs are utilized to learn latent representations within a graph-based framework, promoting unsupervised learning while unveiling the underlying data structure. The resultant embeddings are pivotal for downstream tasks like clustering and visualization, encapsulating the interactions within multimodal time series data effectively. Furthermore, this work incorporates transfer learning with pretrained transformers to harness extensive knowledge from large datasets, adapting it to multimodal time series analysis. This strategy excels in capturing long-range dependencies, thereby augmenting generalization and performance in data-scarce scenarios. Bayesian state-space models are employed to elucidate the temporal dynamics and uncertainties of time series data, offering a robust framework for probabilistic inference and enhancing the interpretability and reliability of forecasting and anomaly detection. The efficacy of the proposed model is rigorously evaluated using diverse datasets, including the Yahoo! Stock Dataset, Forest Cover Dataset, and an empirical collection of 100k time series data samples. The results demonstrate a significant leap in performance metrics, including a 9.5% increase in precision, 8.5% boost in accuracy, 8.3% rise in recall, 10.4% reduction in delay, 9.4% enhancement in AUC, and a 5.9% improvement in specificity, alongside superior pre-emption capabilities compared to existing methods. This work not only addresses the pressing need for advanced multimodal time series analysis techniques but also sets a new benchmark for efficiency and accuracy. The integration of GATs, VGAEs, transfer learning with pretrained transformers, and Bayesian state-space models presents a formidable approach that significantly advances the field, offering profound impacts on a wide array of applications.

Attention-guided variational graph autoencoders reveal heterogeneity in spatial transcriptomics.

The latest breakthroughs in spatially resolved transcriptomics technology offer comprehensive opportunities to delve into gene expression patterns within the tissue microenvironment. However, the precise identification of spatial domains within tissues remains challenging. In this study, we introduce AttentionVGAE (AVGN), which integrates slice images, spatial information and raw gene expression while calibrating low-quality gene expression. By combining the variational graph autoencoder with multi-head attention blocks (MHA blocks), AVGN captures spatial relationships in tissue gene expression, adaptively focusing on key features and alleviating the need for prior knowledge of cluster numbers, thereby achieving superior clustering performance. Particularly, AVGN attempts to balance the model's attention focus on local and global structures by utilizing MHA blocks, an aspect that current graph neural networks have not extensively addressed. Benchmark testing demonstrates its significant efficacy in elucidating tissue anatomy and interpreting tumor heterogeneity, indicating its potential in advancing spatial transcriptomics research and understanding complex biological phenomena.

Abstract 4912: Unsupervised detection of stromal phenotypes with distinct fibrogenic and inflamed properties in NSCLC

Abstract Background: Understanding the composition of cancer-associated stroma (CAS) is vital, as the number and location of immune cells and fibroblasts, as well as the degree of extracellular matrix deposition, have implications for cancer progression and response to treatment, including in non-small cell lung cancer (NSCLC). Manual analysis of CAS does not fully describe the stromal milieu, especially from a spatial perspective, and is highly subjective. To this end, we have developed an unsupervised machine learning (ML) model to characterize the CAS in NSCLC from hematoxylin and eosin (H&E) stained whole slide images (WSI) at scale. Methods: PathExploreTM models were deployed to predict stromal tissue and cell types, while another ML model was used to detect collagen fibers from H&E stained WSIs from the TCGA LUAD (N=536) and LUSC (N=464) datasets. Stroma was divided into small regions (median = 0.02 mm2), and 88 features characterizing cell distribution, tissue composition and fiber density were extracted from each region. Graphs were generated connecting neighboring regions (nodes), and an unsupervised variational graph auto-encoder (VGAE) model was trained to learn 8 latent features through dimensionality reduction. Stromal phenotypes were then derived from the latent features using k-means clustering. The fraction of each phenotype in the stroma was correlated against immune- and stroma-related gene expression signatures (GES) and overall survival (OS). Results: Deployment of VGAE on LUAD and LUSC WSIs revealed three distinct stromal phenotypes - P0, P1 and P2. Fibroblast density was elevated in P0 and P1 regions (p<0.001), immune cell density was elevated in P2 regions (p<0.001), and collagen fiber intensity was highest in P1 regions (p<0.001). P2 enrichment was correlated with elevated expression of the T cell-inflamed gene expression profile (TGEP; Spearman ρ = 0.43 in LUAD; ρ = 0.27 in LUSC) and with improved OS (HR = 0.696; 95% CIs: 0.571-0.847 in LUSC). Conversely, P1 enrichment was positively associated with a transforming growth factor-β-induced cancer associated fibroblast GES (TGFβ-CAF: ρ = 0.19 in LUAD and ρ = 0.12 in LUSC) and poor OS (HR = 1.358; 95% CIs: 1.149-1.603 in LUSC). These phenotypes are consistent with fibroblast-enriched, collagen-depleted stroma (P0), collagen-rich, fibroblast-enriched tumor-promoting stroma (P1), and immune cell-enriched, tumor-suppressive stroma (P2). Conclusions: We describe an unsupervised, data-driven method of predicting stromal regions with discrete patterns of cell composition and collagen deposition in NSCLC. This approach identified three phenotypes of NSCLC stroma. These results highlight the ability of ML models to characterize and find meaningful patterns within the cell, tissue, and matrix components of a tumor. This work provides further evidence of the potential of ML to discover novel precision medicine biomarkers in NSCLC. Citation Format: Neel Patel, Nhat Le, Tan Nguyen, Fedaa Najdawi, Sandhya Srinivasan, Adam Stanford-Moore, Deeksha Kartik, Jun Zhang, Jacqueline Brosnan-Cashman, Robert Egger, Justin Lee, Matthew Bronnimann. Unsupervised detection of stromal phenotypes with distinct fibrogenic and inflamed properties in NSCLC [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 4912.

Online course evaluation model based on graph auto-encoder

In the post-epidemic era, online learning has gained increasing attention due to the advancements in information and big data technology, leading to large-scale online course data with various student behaviors. Online data mining has become a popular and important way of extracting valuable insights from large amounts of data. However, previous online course analysis methods often focused on individual aspects of the data and neglected the correlation among the large-scale learning behavior data, which can lead to an incomplete understanding of the overall learning behavior and patterns within the online course. To solve the problems, this paper proposes an online course evaluation model based on a graph auto-encoder. In our method, the features of collected online course data are used to construct K-Nearest Neighbor(KNN) graphs to represent the association among the courses. Then the variational graph auto-encoder(VGAE) is introduced to learn the useful implicit features. Finally, we feed the learned implicit features into unsupervised and semi-supervised downstream tasks for online course evaluation, respectively. We conduct experiments on two datasets. In the clustering task, our method showed a more than tenfold increase in the Calinski-Harabasz index compared to unoptimized features, demonstrating significant structural distinction and group coherence. In the classification task, compared to traditional methods, our model exhibited an overall performance improvement of about 10%, indicating its effectiveness in handling complex network data.

Recognition of Yuan blue and white porcelain produced in Jingdezhen based on graph anomaly detection combining portable X-ray fluorescence spectrometry

The blue and white porcelain produced in Jingdezhen during China’s Yuan Dynasty is an outstanding cultural heritage of ceramic art that has attracted wide attention for its identification. However, the traditional visual identification method is susceptible to misjudgment, thermoluminescence dating damages the samples, and the methods based on chemical analysis are limited by the accuracy and specificity of the elemental features. In this paper, we address the identification challenge by using machine learning techniques combined with portable X-ray Fluorescence Spectrometer (pXRF) analysis. We collect a large dataset of chemical compositions of Yuan blue and white porcelain from Jingdezhen using pXRF, and propose a graph anomaly detection method based on gradient attention map (GRAM) to identify the porcelain from different dynasties. We treat the porcelain produced in the Yuan dynasty as normal samples and those from other dynasties as abnormal samples. For GRAM, we merely train the variational graph autoencoder (VGAE) model with normal graphs and then use its encoder to extract graph features and compute the anomaly scores by utilizing the GRAM of the graph representations with respect to the node feature embeddings. Finally, we compare GRAM with state-of-the-art graph anomaly detection techniques and show that it achieves superior performance.

Application of Variational Graph Autoencoder in Traction Control of Energy-Saving Driving for High-Speed Train

In a high-speed rail system, the driver repeatedly adjusts the train’s speed and traction while driving, causing a high level of energy consumption. This also leads to the instability of the train’s operation, affecting passengers’ experiences and the operational efficiency of the system. To solve this problem, we propose a variational graph auto-encoder (VGAE) model using a neural network to learn the posterior distribution. This model can effectively capture the correlation between the components of a high-speed rail system and simulate drivers’ operating state accurately. The specific traction control is divided into two parts. The first part employs an algorithm based on the K-Nearest Neighbors (KNN) algorithm and undersampling to address the negative impact of imbalanced quantities in the training dataset. The second part utilizes a variational graph autoencoder to derive the initial traction control of drivers, thereby predicting the energy performance of the drivers’ operation. An 83,786 m long high-speed train driving section is used as an example for verification. By using a confusion matrix for our comparative analysis, it was concluded that the energy consumption is approximately 18.78% less than that of manual traction control. This shows the potential and effect of the variational graph autoencoder model for optimizing energy consumption in high-speed rail systems.

MAVGAE: a multimodal framework for predicting asymmetric drug–drug interactions based on variational graph autoencoder

Drug-drug interactions refer to the phenomena wherein the potency, duration, or effectiveness of one or multiple drugs undergo alterations of varying degrees as a result of their concurrent or sequential usage. The accurate identification of potential drug interactions plays a pivotal role in mitigating the risks associated with drug administration in patients, it also helps in minimizing the likelihood of hazardous situations arising during a patient’s course of treatment. However, researchers have found that there is a problem of asymmetric drug interactions, where one drug may affect another but not vice versa. This adds to the difficulty of prediction, so in polypharmacy, the order of drug administration is critical to efficacy and safety, and few current studies predict asymmetric DDIs. Aiming at the above problems, we propose a framework based on multimodal data and a variational graph autoencoder named MAVGAE for predicting asymmetric drug interactions. The framework initially encodes multimodal data into low-dimensional representations and then utilizes a variational graph autoencoder for encoding and decoding. During the model training process, supervised learning is employed for the classification task with the incorporation of heterogeneity information, ensuring accurate prediction of drug interactions. Experimental validation on a large-scale drug dataset demonstrates the framework’s high accuracy and reliability in predicting non-symmetrical drug interactions, offering effective support and guidance for drug research.

Prediction of Associations between Nanoparticle, Drug and Cancer Using Variational Graph Autoencoder

Predicting implicit drug-disease associations is critical to the development of new drugs, with the aim of minimizing side effects and development costs. Existing drug-disease prediction methods typically focus on either single or multiple drug-disease networks. Recent advances in nanoparticles particularly in cancer research show improvements in bioavailability and pharmacokinetics by reducing toxic side effects. Thus, the interaction of the nanoparticles with drugs and diseases tends to improve during the development phase. In this study, it presents a variational graph autoencoder model to the cell-specific drug delivery data, including the class interactions between nanoparticle, drug, and cancer types as a knowledge base for targeted drug delivery. The cell-specific drug delivery data is transformed into a bipartite graph where relations only exist between sequences of these class interactions. Experimental results show that the knowledge graph enhanced Variational Graph Autoencoder model with VGAE-ROC-AUC (0.9627) and VGAE-AP (0.9566) scores performs better than the Graph Autoencoder model.

Unsupervised spatially embedded deep representation of spatial transcriptomics

Optimal integration of transcriptomics data and associated spatial information is essential towards fully exploiting spatial transcriptomics to dissect tissue heterogeneity and map out inter-cellular communications. We present SEDR, which uses a deep autoencoder coupled with a masked self-supervised learning mechanism to construct a low-dimensional latent representation of gene expression, which is then simultaneously embedded with the corresponding spatial information through a variational graph autoencoder. SEDR achieved higher clustering performance on manually annotated 10 × Visium datasets and better scalability on high-resolution spatial transcriptomics datasets than existing methods. Additionally, we show SEDR’s ability to impute and denoise gene expression (URL: https://github.com/JinmiaoChenLab/SEDR/).

Graph Domain Adaptation: A Generative View

Recent years have witnessed tremendous interest in deep learning on graph-structured data. Due to the high cost of collecting labeled graph-structured data, domain adaptation is important to supervised graph learning tasks with limited samples. However, current graph domain adaptation methods are generally adopted from traditional domain adaptation tasks, and the properties of graph-structured data are not well utilized. For example, the observed social networks on different platforms are controlled not only by the different crowds or communities but also by domain-specific policies and background noise. Based on these properties in graph-structured data, we first assume that the graph-structured data generation process is controlled by three independent types of latent variables, i.e., the semantic latent variables, the domain latent variables, and the random latent variables. Based on this assumption, we propose a disentanglement-based unsupervised domain adaptation method for the graph-structured data, which applies variational graph auto-encoders to recover these latent variables and disentangles them via three supervised learning modules. Extensive experimental results on two real-world datasets in the graph classification task reveal that our method not only significantly outperforms the traditional domain adaptation methods and the disentangled-based domain adaptation methods but also outperforms the state-of-the-art graph domain adaptation algorithms. The code is available at https://github.com/rynewu224/GraphDA .

A recommendation model for e-commerce platforms oriented to explicit information compensation and hidden information mining

In an e-commerce platform recommendation system, accurately mining users’ preferences and hidden information has always been an important initiative. In this study, based on the potential preferences and hidden characteristics of users, we propose a recommendation model for e-commerce platforms oriented to explicit information compensation and hidden information mining. First, considering the advantages of the VGAE (variational Graph Auto-Encoder) in reconstructing data samples, we propose an EI-VGAE (Explicit Information-Variational Graph Auto-Encoder) to compensate for the lack of explicit feedback. Second, to address the problem that hidden information in e-commerce platforms is difficult to mine, an xDeepFM (eXtremely Deep Factorization Machine) is used to jointly learn higher-order interaction features explicitly and implicitly. A time decay function is also introduced to reduce the impact of higher-order interaction features on the representation of hidden information. Finally, considering the advantages of the attention mechanism for obtaining implicit relational attention and the quantification of the user’s degree of preference in local representation, a GAT (Graph Attention Network)-based recommendation model for the e-commerce platform EI-GAT (Explicit and Implicit Graph Attention Network) is proposed. Our experiments show that the proposed method effectively alleviates the problem of low recommendation accuracy owing to insufficient explicit feedback from consumers and further improves recommendation accuracy by quantifying user preferences.

Assembling spatial clustering framework for heterogeneous spatial transcriptomics data with GRAPHDeep.

Spatial clustering is essential and challenging for spatial transcriptomics' data analysis to unravel tissue microenvironment and biological function. Graph neural networks are promising to address gene expression profiles and spatial location information in spatial transcriptomics to generate latent representations. However, choosing an appropriate graph deep learning module and graph neural network necessitates further exploration and investigation. In this article, we present GRAPHDeep to assemble a spatial clustering framework for heterogeneous spatial transcriptomics data. Through integrating 2 graph deep learning modules and 20 graph neural networks, the most appropriate combination is decided for each dataset. The constructed spatial clustering method is compared with state-of-the-art algorithms to demonstrate its effectiveness and superiority. The significant new findings include: (i) the number of genes or proteins of spatial omics data is quite crucial in spatial clustering algorithms; (ii) the variational graph autoencoder is more suitable for spatial clustering tasks than deep graph infomax module; (iii) UniMP, SAGE, SuperGAT, GATv2, GCN, and TAG are the recommended graph neural networks for spatial clustering tasks; and (iv) the used graph neural network in the existent spatial clustering frameworks is not the best candidate. This study could be regarded as desirable guidance for choosing an appropriate graph neural network for spatial clustering. The source code of GRAPHDeep is available at https://github.com/narutoten520/GRAPHDeep. The studied spatial omics data are available at https://zenodo.org/record/8141084.

Leverage Variational Graph Representation for Model Poisoning on Federated Learning.

This article puts forth a new training data-untethered model poisoning (MP) attack on federated learning (FL). The new MP attack extends an adversarial variational graph autoencoder (VGAE) to create malicious local models based solely on the benign local models overheard without any access to the training data of FL. Such an advancement leads to the VGAE-MP attack that is not only efficacious but also remains elusive to detection. VGAE-MP attack extracts graph structural correlations among the benign local models and the training data features, adversarially regenerates the graph structure, and generates malicious local models using the adversarial graph structure and benign models' features. Moreover, a new attacking algorithm is presented to train the malicious local models using VGAE and sub-gradient descent, while enabling an optimal selection of the benign local models for training the VGAE. Experiments demonstrate a gradual drop in FL accuracy under the proposed VGAE-MP attack and the ineffectiveness of existing defense mechanisms in detecting the attack, posing a severe threat to FL.

Efficient Spiking Variational Graph Auto-Encoders for Unsupervised Graph Representation Learning Tasks

Efficient Spiking Variational Graph Auto-Encoders for Unsupervised Graph Representation Learning Tasks

Identifying disease-related microbes based on multi-scale variational graph autoencoder embedding Wasserstein distance

BackgroundEnormous clinical and biomedical researches have demonstrated that microbes are crucial to human health. Identifying associations between microbes and diseases can not only reveal potential disease mechanisms, but also facilitate early diagnosis and promote precision medicine. Due to the data perturbation and unsatisfactory latent representation, there is a significant room for improvement.ResultsIn this work, we proposed a novel framework, Multi-scale Variational Graph AutoEncoder embedding Wasserstein distance (MVGAEW) to predict disease-related microbes, which had the ability to resist data perturbation and effectively generate latent representations for both microbes and diseases from the perspective of distribution. First, we calculated multiple similarities and integrated them through similarity network confusion. Subsequently, we obtained node latent representations by improved variational graph autoencoder. Ultimately, XGBoost classifier was employed to predict potential disease-related microbes. We also introduced multi-order node embedding reconstruction to enhance the representation capacity. We also performed ablation studies to evaluate the contribution of each section of our model. Moreover, we conducted experiments on common drugs and case studies, including Alzheimer’s disease, Crohn’s disease, and colorectal neoplasms, to validate the effectiveness of our framework.ConclusionsSignificantly, our model exceeded other currently state-of-the-art methods, exhibiting a great improvement on the HMDAD database.

A contrastive variational graph auto-encoder for node clustering

Variational Graph Auto-Encoders (VGAEs) have been widely used to solve the node clustering task. However, the state-of-the-art methods have numerous challenges. First, existing VGAEs do not account for the discrepancy between the inference and generative models after incorporating the clustering inductive bias. Second, current models are prone to degenerate solutions that make the latent codes match the prior independently of the input signal (i.e., Posterior Collapse). Third, existing VGAEs overlook the effect of the noisy clustering assignments (i.e., Feature Randomness) and the impact of the strong trade-off between clustering and reconstruction (i.e., Feature Drift). To address these problems, we formulate a variational lower bound in a contrastive setting. Our lower bound is a tighter approximation of the log-likelihood function than the corresponding Evidence Lower BOund (ELBO). Thanks to a newly identified term, our lower bound can escape Posterior Collapse and has more flexibility to account for the difference between the inference and generative models. Additionally, our solution has two mechanisms to control the trade-off between Feature Randomness and Feature Drift. Extensive experiments show that the proposed method achieves state-of-the-art clustering results on several datasets. We provide strong evidence that this improvement is attributed to four aspects: integrating contrastive learning and alleviating Feature Randomness, Feature Drift, and Posterior Collapse.

HetFCM: functional co-module discovery by heterogeneous network co-clustering.

Functional molecular module (i.e., gene-miRNA co-modules and gene-miRNA-lncRNA triple-layer modules) analysis can dissect complex regulations underlying etiology or phenotypes. However, current module detection methods lack an appropriate usage and effective model of multi-omics data and cross-layer regulations of heterogeneous molecules, causing the loss of critical genetic information and corrupting the detection performance. In this study, we propose a heterogeneous network co-clustering framework (HetFCM) to detect functional co-modules. HetFCM introduces an attributed heterogeneous network to jointly model interplays and multi-type attributes of different molecules, and applies multiple variational graph autoencoders on the network to generate cross-layer association matrices, then it performs adaptive weighted co-clustering on association matrices and attribute data to identify co-modules of heterogeneous molecules. Empirical study on Human and Maize datasets reveals that HetFCM can find out co-modules characterized with denser topology and more significant functions, which are associated with human breast cancer (subtypes) and maize phenotypes (i.e., lipid storage, drought tolerance and oil content). HetFCM is a useful tool to detect co-modules and can be applied to multi-layer functional modules, yielding novel insights for analyzing molecular mechanisms. We also developed a user-friendly module detection and analysis tool and shared it at http://www.sdu-idea.cn/FMDTool.