Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Non-standard multilayer graph clustering methods are needed for assigning clusters to a common multilayer node set and for combining information from each layer. This paper present…
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48 results for “multilayer graphs”
Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theo…
Improved graph-based multiclass classification for multilayer data.
problem Efficient classification of multilayer data with limited labeled examples.
method Generalized diffuse interface methods applied to multilayer graphs, using spectral decomposition and fast matrix-vector products.
result Highly scalable and efficient classification for large, high-dimensional data sets.
We study the task of semi-supervised learning on multilayer graphs by taking into account both labeled and unlabeled observations together with the information encoded by each individual graph layer. We propose a regularizer based on the generalized matrix mean, which is a one-parameter family of matrix means that incl…
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.
Multilayer graphs encode different kind of interactions between the same set of entities. When one wants to cluster such a multilayer graph, the natural question arises how one should merge the information different layers. We introduce in this paper a one-parameter family of matrix power means for merging the Laplacia…
PCGs encompass a broader range of neural networks.
problem Understanding the broader scope of neural network models.
method Proving PCGs as a superset of feedforward neural networks.
result PCGs represent a wider class of neural network models.
A network community detection method with integration of data from multiple layers and node attributesphysics.soc-ph
A method for community detection in multilayer networks using data matrices.
problem Community detection in multilayer networks with various node attributes.
method Data matrix representation and regular decomposition method extension for compression.
result Method identifies community structures well-aligned with real-world network hierarchies.
Proposes graph neural network layers for manifold-valued graphs.
problem Graphs with features in a Riemannian manifold.
method Diffusion layer and tangent multilayer perceptron.
result Outperforms state-of-the-art networks on Alzheimer's classification.
Dynamic transportation networks have been analyzed for years by means of static graph-based indicators in order to study the temporal evolution of relevant network components, and to reveal complex dependencies that would not be easily detected by a direct inspection of the data. This paper presents a state-of-the-art …
Model predicts loan default risk using dynamic multilayer graph neural networks.
problem Credit risk assessment through borrower connections.
method Dynamic multilayer graph neural network with attention mechanism.
result Attention mechanism improves model performance.
A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscs.LG
New method constructs equivariant neural networks for arbitrary matrix groups.
problem Challenges in constructing equivariant neural networks for complex groups.
method Completely general algorithm for solving equivariant layers of matrix groups.
result Constructs multilayer perceptrons equivariant to multiple groups including O(1,3), O(5), Sp(n), and Rubik's cube group.
Paper perfect clusters sparse, diverse multilayer networks.
problem Clustering sparse, diverse multilayer networks.
method Tensor-based methodology pooling all layers' information.
result Achieves perfect clustering under sparser conditions than previous models.
Develops rMultiNet R package for multilayer network analysis.
problem Analyzing multilayer network data.
method Two frameworks: MMSBM and MMLSM for generating multilayer networks; methods for node and layer embedding; clustering.
result Provides tools for multilayer network analysis.
Non-local GNNs improve performance on disassortative graphs.
problem Efficiency and performance issues in local aggregation for disassortative graphs.
method Proposes a non-local aggregation framework with attention-guided sorting.
result Significantly outperforms previous methods on disassortative graphs.
Graph convolutional kernel networks generalize CNNs to graph data.
problem Representing graph-structured data for machine learning.
method Convolutional kernel networks applied to graph data.
result Competitive performance on graph classification benchmarks.
Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from group theory, this paper proves the universality of a broad class of equivariant M…
New method breaks symmetry in neural networks, improving sample efficiency.
problem Symmetry in neural networks limits their ability to learn unique features.
method Introduces 'relaxed equivariance' to overcome symmetry limitations.
result Equivariant multilayer perceptrons (E-MLPs) can now break symmetry at the sample level.
Inverse design of multilayer nanoparticles using artificial neural networks and genetic algorithmeess.SP
New method designs multilayer nanoparticles using AI.
problem Difficult to design multilayer nanoparticles by trial and error.
method Combines genetic algorithm and neural network for inverse design.
result Successfully designs multilayer nanoparticles efficiently.
Network data appears in very diverse applications, like biological, social, or sensor networks. Clustering of network nodes into categories or communities has thus become a very common task in machine learning and data mining. Network data comes with some information about the network edges. In some cases, this network…
The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean settings such as graphs. Our work builds upon these constructions by introducin…
Paper analyzes GCNN sensitivity to probabilistic graph perturbations.
problem Investigating how GCNNs handle probabilistic graph errors.
method Establishes error bounds and linear relationships between GSO perturbations and GCNN outputs.
result GCNNs maintain stability under graph edge perturbations if GSO errors are bounded.
We propose a method for simultaneously detecting shared and unshared communities in heterogeneous multilayer weighted and undirected networks. The multilayer network is assumed to follow a generative probabilistic model that takes into account the similarities and dissimilarities between the communities. We make use of…
New integral transforms solve multilayer heat equations.
problem Solving multilayer heat equations with moving boundaries.
method Expanding Dirac delta function in eigenfunctions, constructing oscillating integral transforms.
result Semi-analytical solutions for various problems.
Paper introduces TSSDMN for modeling dynamic multilayer networks.
problem Capturing temporal and cross-layer dynamics in multilayer networks.
method Tensor State Space Model (TSSDMN) using symmetric Tucker decomposition.
result TSSDMN uniquely captures temporal dynamics within and across layers.
Extends random dot product graph model to handle multiple graphs.
problem Modeling and analyzing multiple graphs with shared nodes.
method Jointly embed adjacency matrices into a latent space.
result Node representations converge to latent positions with Gaussian error.
We propose a novel learning method for multilayered neural networks which uses feedforward supervisory signal and associates classification of a new input with that of pre-trained input. The proposed method effectively uses rich input information in the earlier layer for robust leaning and revising internal representat…
ALMA improves clustering of multilayer networks.
problem Clustering multilayer networks with distinct layers and communities.
method Alternating minimization algorithm (ALMA) for simultaneous layer partition and community estimation.
result ALMA achieves higher accuracy than TWIST in clustering multilayer networks.
New method constructs multilayer networks from financial data, capturing dependencies across different risk factors.
problem Difficult construction of multilayer networks, neglecting time delays and interdependencies.
method Tucker tensor autoregression for direct multilayer network construction.
result Captures within and between connections, identifies strong interconnections between volumes and prices layers.
New algorithm assesses credit risk in multilayer networks over time.
problem Quantifying evolving credit risk in complex, interconnected networks.
method Personalized PageRank algorithm for multilayer networks.
result Credit risk evolves and propagates through multilayer networks over time.
Multilayer networks are a useful data structure for simultaneously capturing multiple types of relationships between a set of nodes. In such networks, each relational definition gives rise to a layer. While each layer provides its own set of information, community structure across layers can be collectively utilized to…
Community detection in temporal multilayer networks, with an application to correlation networksphysics.soc-ph
Networks are a convenient way to represent complex systems of interacting entities. Many networks contain "communities" of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilay…
Novel model detects communities in noisy multilayer networks.
problem Understanding communities in noisy multilayer networks.
method Hierarchical variational inference for joint detection and typologizing.
result Discover communities of subjects with co-occurrent psychopathologies.
We propose a new type of hidden layer for a multilayer perceptron, and demonstrate that it obtains the best reported performance for an MLP on the MNIST dataset.
SDP approach recovers communities in multilayer hypergraphs from aggregated similarity matrices.
problem Community recovery in multilayer hypergraphs using aggregated similarity matrices.
method Semidefinite programming (SDP) approach.
result Information-theoretic conditions for exact recovery in both assortative and disassortative cases.
Global convergence of multilayer neural networks proven for any depth.
problem Global convergence of multilayer neural networks in the mean field regime.
method Mean field limit framework, neuronal embedding, bidirectional diversity condition.
result Global convergence for multilayer networks of any depths, including correlated initializations.
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.
Scalable and Robust Sparse Subspace Clustering Using Randomized Clustering and Multilayer Graphscs.CV
Sparse subspace clustering (SSC) is one of the current state-of-the-art methods for partitioning data points into the union of subspaces, with strong theoretical guarantees. However, it is not practical for large data sets as it requires solving a LASSO problem for each data point, where the number of variables in each…
A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation at node/edge or substructure level. However, many real life challenges such as ti…
Graph neural networks struggle with heterophily, but new designs improve their performance.
problem Graph neural networks struggle with heterophily (networks where connected nodes may have different class labels and dissimilar features).
method Ego- and neighbor-embedding separation, higher-order neighborhoods, and combination of intermediate representations.
result The identified designs increase the accuracy of GNNs by up to 40% and 27% over models without them on synthetic and real networks with heterophily, respectively.
Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale fe…
Flexible inference model for multilayer networks with heterogeneous data.
problem Complexity of heterogeneous data in networked datasets.
method Probabilistic generative model using Bayesian framework and Laplace matching.
result Effective detection of overlapping community structures and prediction tasks.
A framework for multilayer networks predicts links without shared structures.
problem Link prediction in multilayer networks without shared structures.
method Bi-level model averaging with -fold cross-validation.
result Framework outperforms existing methods in predictive accuracy and robustness.
Learning Latent Graph Geometry via Fixed-Point Schrödinger-Type Activation: A Theoretical Studycs.LG
Study neural architectures on learned latent graphs using Schrödinger dynamics.
problem Understanding neural architectures on learned latent graphs.
method Optimizes over stratified moduli space of weighted graphs with Kähler-Hessian metric.
result Multilayer stationary networks are equivalent to global stationary problems on supra-graphs.
Proposes a new algorithm to estimate invariant subspaces across multilayer networks.
problem Estimating invariant subspaces across heterogeneous multiple networks.
method Bias-corrected joint spectral embedding algorithm that recursively calibrates diagonal bias and iteratively updates the subspace estimator.
result Established entrywise subspace perturbation bound and entrywise eigenvector central limit theorem for the algorithm.
A novel multilayer network approach for text analysis.
problem Clustering documents and finding topics in large collections with metadata and hyperlinks.
method Multilayer Networks and Stochastic Block Models applied to multiple data types.
result Taking into account multiple types of information improves topic and document clustering.
Spectral graph sparsification preserves geometry of GNN embeddings.
problem Maintaining geometric properties of graph neural network embeddings during sparsification.
method Proving spectral sparsification preserves squared pairwise distances, class means, and covariance structure in embedding space.
result Spectral sparsification preserves the geometry of learned embeddings in GNNs.
A new method for neural network initialization using graph degeneracy.
problem Improving neural network performance through better initialization.
method Adapted k-hypercore decomposition for neural network initialization.
result k-hypercore outperforms state-of-the-art initialization methods.