FINGER computes von Neumann graph entropy efficiently for online graph sequence analysis.
problem Efficiently compute von Neumann graph entropy for online graph sequence analysis.
method Fast Incremental von Neumann Graph Entropy (FINGER) framework.
result FINGER reduces VNGE computation complexity from cubic to linear.
DynGraph2Seq predicts health stages from user activity graphs in online forums.
problem Predicting health stages from changing user activities in online forums.
method Formulated user activities as dynamic graphs, used DynGraph2Seq model with hierarchical attention.
result Demonstrated effectiveness and interpretability of DynGraph2Seq.
The curve graph and related graphs are hyperbolic and have quasi-tree fibers.
problem Understanding the structure of the curve graph and related graphs.
method Analyzing a sequence of graphs with Lipschitz maps and proving hyperbolicity and quasi-tree properties.
result The graphs in the sequence are hyperbolic and have quasi-tree fibers, leading to bounds on asymptotic dimension and acylindrical actions.
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and many other parametric and nonparametric Bayesian models fall within the remit of …
Grid homology theory for spatial graphs extends skein sequence.
problem No specific problem stated; focuses on extending a sequence.
method Defined grid homology theory for spatial graphs and extended skein sequence.
result Skein exact sequence extended to grid homology for spatial graphs.
The paper studies the graph geometry of finite groups, creating a dataset and analyzing its properties.
problem Understanding how group-theoretic structure is reflected in Cayley graph observables.
method Construction of a dataset of Cayley graphs for groups of order up to 767, analysis of graph statistics, and comparison of model performance.
result Graph statistics are highly informative for predicting group properties, and GNNs can recover substantial structural signal.
A new method for fast graph embedding using diffusion graphs.
problem Efficiently generating graph embeddings for large networks.
method Diffusion graphs for rapid vertex sequence generation.
result Improved accuracy and performance with higher edge density.
Graph2Seq converts graph inputs to sequences with attention-based neural networks.
problem Converting graph inputs to sequences for machine learning tasks.
method Graph-to-sequence neural encoder-decoder model with attention-based LSTM.
result Achieves state-of-the-art performance on various tasks.
Paper proposes AR model for graph sequences.
problem Predicting sequences of graphs with variable topology.
method Formalizes AR model for graphs using GNN to learn and predict next graph.
result Significantly better performance on synthetic graph generation problems.
Graphs from van der Corput sequence embed into Chamanara surface.
problem Embedding graphs from van der Corput sequence into surfaces.
method Constructed 4-regular graphs from van der Corput sequence and Kronecker sequence, embedded into torus and Chamanara surface. result Graphs from van der Corput sequence embed into Chamanara surface with one edge removal.
AutoGraph uses transformers to efficiently generate graphs as sequences.
problem Efficiently generating large, sparse graphs without expensive node features.
method Flattening graphs into sequences and using decoder-only transformers.
result AutoGraph achieves state-of-the-art performance on synthetic and molecular benchmarks.
Graphs represent gene segment organization, revealing complex interrelationships in a scrambled genome.
problem Understanding gene segment organization and interrelationships in a scrambled genome.
method Directed graphs representing gene segments and their relationships, with graph properties mapped to higher-dimensional space for analysis.
result Emerging star-like structures indicate complex interrelationships, including segments from multiple genes interleaving or overlapping.
Graph classification model learns sequentially from graph structure.
problem Graph classification based on structural information.
method Sequential embedding and variational regularization.
result State-of-the-art classification results on molecular datasets.
Develops a hybrid model for text summarization.
problem Summarizing long text sequences concisely.
method Extends sequence encoders with a graph component to handle long-distance relationships in text.
result Hybrid models outperform pure sequence or graph models on summarization tasks.
New method clusters directed graphs using Koopman operators.
problem Challenges in clustering directed graphs, especially complex eigenvalues and lack of cluster definition.
method Relate graph Laplacians to transfer operators and metastable sets in stochastic systems, derive clustering algorithms for directed and time-evolving graphs.
result Clusters can be interpreted as coherent sets, useful for analyzing transport and mixing processes.
Framework learns dynamic graph attributes and links co-evolution.
problem Forecasting change of node attributes and link formation in dynamic graphs.
method CoEvoGNN framework with temporal self-attention and joint optimization.
result Framework outperforms baselines on predicting unseen graph snapshots.
Sequencer algorithm detects main trends in complex datasets.
problem Detecting simple phenomena in complex data.
method Constructs graphs from data similarities, identifies elongated trends.
result Sequencer outperforms t-SNE and UMAP in identifying main trends.
New method approximates partition function of graphical models using gauge functions and polynomials.
problem Computing the partition function of graphical models is computationally challenging.
method Combines gauge function technique with real stable polynomials to approximate partition function.
result Belief Propagation estimations in the sequence do not decrease and low-bound the partition function.
SENSE enhances node sequences in graphs using vector embeddings.
problem Efficiently capturing graph node sequences for applications.
method SENSE-S learns node embeddings and composes them for sequences, preserving node order.
result SENSE-S increases multi-label classification and link-prediction accuracy by up to 50% and 78% respectively.
Learned factor graphs improve inference from time sequences using neural networks.
problem Inference from time sequences with limited labeled data.
method Combines model-based algorithms and data-driven ML tools for stationary time sequences.
result Learned factor graphs can accurately infer from small training sets.
A planning mechanism improves sequence-to-sequence model performance.
problem Improving sequence-to-sequence model performance for tasks like translation and graph analysis.
method Developed a model that plans ahead using attention and differentiable operations.
result Outperforms strong baselines on character-level translation, graph analysis, and question generation.
Novel graph neural network combines random walks with local message passing.
problem Graph neural networks struggle with long-range dependencies.
method Combines random walks with local message passing in a novel architecture.
result Significant performance improvements on graph benchmarks.
System uses neural networks to prove program equivalence via rewrite rules.
problem Proving equivalence between two dataflow graphs.
method Developed a graph-to-sequence neural network trained on example generation to find semantics-preserving rewrite rules.
result System correctly outputs a rewrite sequence for 96% of program pairs, proving equivalence.
Predicts node sequences in graphs using multi-order network models.
problem Predicting sequences of node traversals in graphs.
method Combines multiple higher-order network models into a multi-order model, fitting and selecting the optimal maximum order.
result Outperforms state-of-the-art algorithms for next-element and full sequence prediction.
New models for graph sequences capture link and community persistence.
problem Difficulties in extending block model results to graph sequences.
method Two models for graph sequences capturing link and community persistence, with efficient inference algorithms.
result Validated suitability of proposed models and methods on synthetic and real instances.
New method extracts dynamics from graph data using DMD in vector-valued spaces.
problem Analyzing nonlinear systems with interdependent observables.
method Formulated Koopman spectral analysis for vector-valued data, developed estimation algorithm.
result Extracts low-dimensional dynamics from graph data.
Graph Hawkes Neural Network forecasts evolving graph sequences.
problem Modeling dynamic graph sequences with complex event types.
method Generalized Hawkes process to neural network, capturing complex event impacts.
result Effective at predicting future events in evolving graph sequences.
New invariants detect a specific graph in spatial webs.
problem Detecting specific graphs in spatial webs.
method Introduced new invariants and used spectral sequences.
result Proved invariants detect the planar theta graph.
The paper extends RDPG model to handle weighted graphs, enabling better analysis of network data.
problem Modeling networks with weighted edges to capture heterogeneous weight distributions.
method Proposes a nonparametric W-RDPG model with latent positions and moment-generating functions.
result Establishes statistical guarantees for estimating nodal latent positions and sampling graphs.
Graph ConvNet improves ncRNA classification accuracy.
problem Classifying non-coding RNA sequences into families.
method Graph Convolutional Network model trained on raw RNA graphs.
result 85.73% accuracy and 85.61% F1-score over 13 classes.
Contradiction graphs reveal VC dimension threshold.
problem Determining VC dimension of concept classes.
method Study contradiction graphs of binary concept classes.
result Single contradiction graph Gm(H) determines VC dimension. GNL addresses dynamic network regression by learning dynamic graph structures and capturing sequence information.
problem Dynamic network regression of multiple inter-connected data entities.
method Graph Neural Lasso (GNL) using gated diffusive units and attention mechanism.
result GNL outperforms existing methods in dynamic network regression tasks.
Graph theory connects automorphisms to cohomology.
problem Understanding automorphism actions on graph cohomology.
method Graph-theoretical interpretation of de Rham cohomology.
result Proves graph analogues of differential geometry results.
Bayesian method detects Markov order in network paths more reliably.
problem Detecting Markov order in constrained categorical sequences.
method Multi-order Bayesian modelling framework.
result Bayesian method detects correct Markov order more reliably than competing methods.
Deep learning model predicts traffic flows across entire network for multiple steps ahead.
problem Accurately forecasting future traffic flows across all network links.
method Spatial-Temporal Sequence to Sequence (STSeq2Seq) model combining seq2seq and graph convolution.
result STSeq2Seq achieves state-of-the-art performance in traffic forecasting.
Finite subgraphs of extension graph are found within a sequence of induced subgraphs.
problem Identifying all finite subgraphs within the extension graph.
method Inductively define a sequence of induced subgraphs through 'doubling along a star'.
result Every finite induced subgraph of the extension graph is isomorphic to an induced subgraph of some Γi. Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is previous work on Graph Neural Networks (Scarselli et al., 2009), which we modif…
This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by an arbitrary graph. Such structured sequences can represent series of frames in v…
Graph WaveNet models spatial-temporal graphs by learning hidden dependencies and long sequences.
problem Capturing hidden spatial dependencies and long-range temporal sequences in graphs.
method Graph WaveNet integrates adaptive dependency matrix learning and stacked dilated 1D convolution.
result Graph WaveNet outperforms existing methods on public traffic network datasets.
Develops a tensor network framework to reduce RNN complexity for high-dimensional sequence modeling.
problem Exponential parameter growth in RNNs for large multidimensional data.
method Embeds a multi-linear graph filter in a tensor network architecture to approximate RNN hidden states.
result Demonstrates superior performance and reduced complexity compared to traditional RNNs.
A natural approach to analyze interaction data of form "what-connects-to-what-when" is to create a time-series (or rather a sequence) of graphs through temporal discretization (bandwidth selection) and spatial discretization (vertex contraction). Such discretization together with non-negative factorization techniques c…
Method detects changes in graph sequences, validated on real data.
problem Identifying changes in graph sequences over time.
method Maps graphs to vectors, applies statistical tests, detects changes.
result Effectiveness validated on real data sets.
Paper uses HGNN to predict stock types from relationships and temporal data.
problem Predicting stock types from complex market data.
method Integrates stock relationships and temporal data using HGNN.
result Effective prediction of stock types with HGNN model.
Sequence feature embedding is a challenging task due to the unstructuredness of sequence, i.e., arbitrary strings of arbitrary length. Existing methods are efficient in extracting short-term dependencies but typically suffer from computation issues for the long-term. Sequence Graph Transform (SGT), a feature embedding …
GTEA learns node representations in temporal interaction graphs.
problem Inductive representation learning on temporal interaction graphs.
method Integrates sequence model with time encoder and self-attention scheme for edge and node embeddings.
result GTEA learns comprehensive node representations capturing temporal and structural characteristics.
Classifies intrinsically linked tournaments by their score sequences.
problem Classifying intrinsically linked tournaments using their score sequences.
method Examining the score sequences of tournaments and identifying linkless sequences.
result The vast majority of score sequences for 8-vertex tournaments are linkless.
A deep learning model predicts traffic conditions over multiple steps.
problem Multistep traffic forecasting on road networks.
method Attention Graph Convolutional Sequence-to-Sequence model (AGC-Seq2Seq) with attention mechanism.
result AGC-Seq2Seq model outperforms other models in multistep traffic prediction.
In this thesis we describe how to estimate the distance spanned in the pants graph by a train track splitting sequence on a surface, up to multiplicative and additive constants. If some moderate assumptions on a splitting sequence are satisfied, each vertex set of a train track in it will represent a vertex of a graph …