Graph embedding is an important approach for graph analysis tasks such as node classification and link prediction. The goal of graph embedding is to find a low dimensional representation of graph nodes that preserves the graph information. Recent methods like Graph Convolutional Network (GCN) try to consider node attri…
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48 results for “multi-layer graphs”
Combines multi-layer graphs to infer global network structure.
problem Leveraging domain knowledge in structure inference for multi-layer graphs.
method Mask combination of multi-layer graphs using optimization.
result Enhanced structure inference through multi-layer graph integration.
GCNs improve multi-layer network classification by expanding the distance between means.
problem Improving multi-layer network classification with graphical information.
method Theoretical and empirical study of graph convolutions in multi-layer networks.
result Graph convolutions expand the classification regime by a factor of .
Modern data analysis pipelines are becoming increasingly complex due to the presence of multi-view information sources. While graphs are effective in modeling complex relationships, in many scenarios a single graph is rarely sufficient to succinctly represent all interactions, and hence multi-layered graphs have become…
Community detection in multi-relational data with restricted multi-layer stochastic blockmodelstat.ML
In recent years there has been an increased interest in statistical analysis of data with multiple types of relations among a set of entities. Such multi-relational data can be represented as multi-layer graphs where the set of vertices represents the entities and multiple types of edges represent the different relatio…
SRR detects early signs of financial crises using multi-layer graphs.
problem Predicting systemic financial transitions from evolving market interactions.
method Systemic Risk Radar (SRR) models financial markets as multi-layer graphs.
result Graph-derived features provide useful early-warning signals compared to feature-based models.
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address the problem of combining different layers of the multi-layer gra…
This study compares GNNs and GA-MLPs, finding GA-MLPs can distinguish graphs but not count walks.
problem Comparing expressive power and graph isomorphism testing capabilities of GNNs and GA-MLPs.
method GA-MLPs augment node features with multi-hop operators and apply MLPs node-wise; GNNs are compared as a baseline.
result GA-MLPs can distinguish almost all non-isomorphic graphs but cannot count attributed walks, unlike GNNs.
A brain can detect outlier just by using only normal samples. Similarly, one-class classification (OCC) also uses only normal samples to train the model and trained model can be used for outlier detection. In this paper, a multi-layer architecture for OCC is proposed by stacking various Graph-Embedded Kernel Ridge Regr…
Develops G-MLKM for better data-target association in constrained spaces.
problem Data-target association problem in constrained spaces with limited sensor information.
method Graph-based multi-layer k-means++ (G-MLKM) method, including MLKM for local space and G-MLKM for general constrained space.
result Improves data-target association accuracy through error correction mechanisms.
New view: Deep GCNs learn to anti-oversmooth during training.
problem Performance drop in deep GCNs due to oversmoothing.
method Interpreted GCN as MLP + graph regularization, analyzed training process.
result Deep GCNs learn to anti-oversmooth during training, not over-smooth.
While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs. Compared to graph kernels, graph neural networks (GNNs) usually achieve better…
Graph-Coupled Oscillator Networks (GraphCON) tackles graph-based learning problems.
problem The oversmoothing problem in Graph Neural Networks (GNNs).
method GraphCON is a novel framework based on discretizations of ODEs modeling oscillators coupled via graph adjacency.
result GraphCON mitigates the oversmoothing problem and exploding/vanishing gradients issues.
Inferencing with network data necessitates the mapping of its nodes into a vector space, where the relationships are preserved. However, with multi-layered networks, where multiple types of relationships exist for the same set of nodes, it is crucial to exploit the information shared between layers, in addition to the …
Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set of weighted and undirected graphs that form a global multilayer graph, where th…
The study estimates the expressiveness of GCNs with bounds on the number of linear regions.
problem Characterizing the expressiveness of graph convolutional networks (GCNs).
method Estimates the number of linear regions for one-layer and multi-layer GCNs.
result GCNs with multiple layers have exponentially more expressivity per parameter than one-layer GCNs.
Graph attention is not always beneficial; conditions for perfect node classification are identified.
problem Understanding when graph attention mechanisms improve node classification performance.
method Theoretical analysis using Contextual Stochastic Block Models (CSBMs).
result Graph attention mechanisms are more effective when structure noise exceeds feature noise, and simpler graph convolution operations are better when feature noise predominates.
Spectral and matrix factorization methods for consistent community detection in multi-layer networksstat.ML
We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general theme, these "intermediate fusion" methods involve obtaining a low column rank matr…
Improved graph generation model for small organic molecules.
problem Graph generation models struggle with matching training distributions and require expensive graph matching.
method Introduced a message passing neural network into the GVAE's encoder and decoder.
result Demonstrated improved graph generation for small organic molecules.
A new model improves the performance of knowledge distillation in GNNs.
problem Inconsistent performance of existing knowledge distillation techniques in GNNs.
method Proposes a new model, Routing-by-Memory (RbM), a form of Mixture-of-Experts (MoE), to address performance concerns.
result Demonstrates experimentally that RbM achieves considerably more consistent performance across multiple datasets.
Clustering and community detection with multiple graphs have typically focused on aligned graphs, where there is a mapping between nodes across the graphs (e.g., multi-view, multi-layer, temporal graphs). However, there are numerous application areas with multiple graphs that are only partially aligned, or even unalign…
Learning representation on graph plays a crucial role in numerous tasks of pattern recognition. Different from grid-shaped images/videos, on which local convolution kernels can be lattices, however, graphs are fully coordinate-free on vertices and edges. In this work, we propose a Gaussian-induced convolution (GIC) fra…
The paper introduces a new loss function to prevent overfitting in semi-supervised graph networks.
problem Overfitting in semi-supervised graph networks trained with cross-entropy loss.
method Proposes an unsupervised manifold smoothness loss to regularize the graph convolutional networks.
result Adding the proposed loss consistently improves performance of graph networks.
Two spectral clustering methods for multi-layer networks are analyzed and compared.
problem Community detection in multi-layer networks.
method Sum and debiased sum of squared adjacency matrices for spectral clustering.
result Debiased sum of squared adjacency matrices outperforms sum of adjacency matrices.
A new GNM model outperforms MLP for tabular data.
problem Learning with tabular data.
method Proposes Graph Neural Machine (GNM) replacing MLP's graph representation with a nearly complete graph and using synchronous message passing.
result GNM outperforms MLP in classification and regression tasks.
We propose a novel framework for graph mean computation.
problem Defining a mean for graph data is difficult.
method Embeddings in the space of smooth graph signal distributions, using the Wasserstein metric.
result Existence and uniqueness of the graph mean established, and an iterative algorithm provided.
Simpler linear models outperform complex GCN encoders for graph tasks.
problem Complex graph autoencoders and variational autoencoders.
method Replacing GCN encoders with one-hop linear models.
result Simpler linear models achieve competitive performance with fewer operations and parameters.
New methods estimate mixed memberships in multi-layer networks.
problem Complex community structure in multi-layer networks.
method Spectral methods using eigen-decomposition of aggregate matrices.
result Theoretical guarantees and empirical validation for mixed membership estimation.
Graph-structured data such as social networks, functional brain networks, gene regulatory networks, communications networks have brought the interest in generalizing deep learning techniques to graph domains. In this paper, we are interested to design neural networks for graphs with variable length in order to solve le…
A scalable deep GMRF model for general graphs improves predictions and uncertainty estimates.
problem Handling generally structured data on graphs efficiently.
method A new multi-layer structure of Deep GMRFs designed for general graphs, enabling efficient training and close-to-exact Bayesian inference.
result Close-to-exact Bayesian inference for latent field predictions with uncertainty estimates.
TWIST algorithm detects communities in multi-layer networks with tensor decomposition.
problem Community detection in multi-layer networks with multiple node-modality relationships.
method Tensor-based TWIST algorithm for global/local node and layer memberships.
result Accurate community detection with small misclassification error as network size increases.
This work tackles asymmetric community estimation in multi-layer directed networks.
problem Estimating different numbers of sender and receiver communities in multi-layer directed networks.
method Proposes a goodness-of-fit test based on the largest singular value of an aggregated normalized residual matrix.
result Develops sequential and ratio-based testing procedures to consistently determine true sender and receiver community numbers.
Proposes a balanced multi-component and multi-layer neural network for efficient function approximation.
problem Accurately and efficiently approximating complex functions with high degrees of freedom and computational cost.
method Inspired by a multi-component approach, MMNN combines single-layer networks with a multi-layer decomposition strategy.
result Significant reduction in training parameters, more efficient training process, and improved accuracy compared to FCNNs or MLPs.
New AMP algorithms improve multi-layer signal reconstruction.
problem Reconstructing signals and hidden variables from multi-layer networks with rotationally invariant weights.
method Developed multi-layer rotationally invariant generalized AMP (ML-RI-GAMP) algorithms and state evolution recursion.
result ML-RI-GAMP outperforms existing methods in terms of lower complexity and similar performance.
Adding node feature kernels improves GCN robustness to graph perturbations.
problem GCNs' robustness to graph perturbations is a concern.
method Introduced random GCN and added node feature kernels to message passing.
result Perturbations of the graph structure can significantly degrade GCN performance.
New model for multi-layer categorical data improves latent class analysis.
problem Traditional latent class analysis for single-layer categorical data is insufficient for multi-layer data.
method Developed a multi-layer latent class model (multi-layer LCM) and three spectral methods for estimation.
result The debiased sum of Gram matrices method performs best in estimating latent classes.
Learned data models based on sparsity are widely used in signal processing and imaging applications. A variety of methods for learning synthesis dictionaries, sparsifying transforms, etc., have been proposed in recent years, often imposing useful structures or properties on the models. In this work, we focus on sparsif…
MXGNet tackles visual reasoning tasks using graph neural networks.
problem Abstract reasoning, especially in the visual domain, is challenging for AI.
method Combines object-level representations, graph neural networks, and multiplex graphs.
result Achieves state-of-the-art accuracy on Euler Diagram Syllogisms and outperforms state-of-the-art models on RPM datasets.
This paper presents a general graph representation learning framework called DeepGL for learning deep node and edge representations from large (attributed) graphs. In particular, DeepGL begins by deriving a set of base features (e.g., graphlet features) and automatically learns a multi-layered hierarchical graph repres…
Structural data from Electronic Health Records as complementary information to imaging data for disease prediction. We incorporate novel weighting layer into the Graph Convolutional Networks, which weights every element of structural data by exploring its relation to the underlying disease. We demonstrate the superiori…
Ripple Walk Training: A Subgraph-based training framework for Large and Deep Graph Neural Networkcs.LG
Ripple Walk Training tackles graph neural network training issues for large and deep graphs.
problem Neighbors explosion, node dependence, and oversmoothing in large and deep GNNs.
method Subgraph-based training framework with Ripple Walk Sampler for high-quality subgraph sampling.
result RWT improves training efficiency and reduces space complexity for deep and large GNNs.
Paper presents ML-VAMP for efficient multi-layer inference with exact performance analysis.
problem Inference in multi-layer deep neural networks with non-convex optimization.
method ML-VAMP algorithm for MAP and MMSE estimates, with performance predictions in high dimensions.
result ML-VAMP achieves Bayes-optimal MSE under certain conditions, providing exact performance characterization.
Algorithm predicts performance of learning in multi-layer networks with matrix-valued hidden variables.
problem Signal recovery and learning in multi-layer neural networks with matrix-valued hidden variables.
method Unified approximation algorithm for MAP and MMSE inference, extending ML-VAMP to handle matrix-valued unknowns.
result Performance of ML-Mat-VAMP algorithm can be predicted in a random large-system limit.
New spectral clustering method for multi-layer networks improves accuracy.
problem Detecting community structure in multi-layer networks.
method Integrative spectral clustering based on adaptive layer aggregation.
result Our methods minimize mis-clustering error and outperform existing methods.
Optimal Clustering of Discrete Mixtures: Binomial, Poisson, Block Models, and Multi-layer Networksmath.ST
Paper optimizes clustering for multi-layer networks and discrete mixtures.
problem Optimizing clustering in multi-layer networks and discrete mixtures.
method Two-stage method: tensor-based initialization and likelihood-based refinement.
result Achieves minimax optimal error rate for multi-layer networks and discrete mixtures.
FMMNN combines sine activations with multi-component, multi-layer structure for high-frequency function approximation.
problem Effective representation and learning of high-frequency features in neural networks.
method Introduces FMMNN with sine-type activations and multi-component, multi-layer structure.
result FMMNN achieves strong accuracy and favorable convergence on oscillatory function-approximation benchmarks.
New method clusters multilayer graphs with missing nodes.
problem Clustering multilayer graphs with missing nodes.
method Proposes a new framework for multilayer graphs with missing nodes, extending clustering methods to handle incomplete data.
result Proves consistency results under the Multi-Layer Stochastic Block Model assumption and highlights promising performance on real datasets.
A usual reinsurance policy for insurance companies admits one or two layers of the payment deductions. Under optimal criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk, this article generalized an optimal stop-loss reinsurance policy to an optimal multi-layer reinsur…