Paper introduces new graph concepts for better modeling of temporal interactions.
problem Graph theory struggles to capture temporal and structural aspects of interactions.
method Generalizes graph concepts to handle both temporal and structural aspects of interactions.
result Formalism allows direct modeling of interactions over time, similar to graph theory.
System helps engineers with concept recognition for SEVA.
problem Recognizing systems engineering concepts for SEVA.
method Token classification task, domain expert labeling, pre-trained model fine-tuning, essential datasets creation, knowledge graph construction.
result System successfully recognizes systems engineering concepts.
Method learns graph from data clusters using FCA.
problem Learning graph representation from multivariate data.
method Uses formal concept analysis (FCA) to extract hierarchical relationships between clusters.
result Empirically shows superior hierarchical structure extraction compared to baseline.
The paper explores heat flow and constants on graphs, proving properties and proposing new concepts.
problem Analyzing heat flow and constants on graphs.
method Introducing concepts, recalling graph theory, and proposing new discrete Morse flows.
result Weak discrete Morse flows for heat flow on finite graphs under suitable assumptions.
A new system recommends specific knowledge concepts in MOOCs based on student interests.
problem MOOCs recommend courses but ignore specific knowledge concepts interests.
method End-to-end graph neural network (ACKRec) that combines content and context information.
result ACKRec effectively recommends knowledge concepts to MOOC students.
This work abstracts deep neural networks into concept graphs for better interpretability in medical tasks.
problem Lack of interpretability in deep learning models, especially in medical domains.
method Developed a graphical representation of medical image processing models to understand concept-based reasoning.
result Extracted a concept-level graph that reveals the decision-making process of deep learning models.
This letter extends the concept of graph-frequency to graph signals that evolve with time. Our goal is to generalize and, in fact, unify the familiar concepts from time- and graph-frequency analysis. To this end, we study a joint temporal and graph Fourier transform (JFT) and demonstrate its attractive properties. We b…
The study evaluates cross-modal knowledge fusion methods.
problem Combining knowledge from text, KGs, and images.
method Evaluation of different fusion methods using embeddings.
result Potential of cross-modal knowledge fusion.
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. Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide …
One of the most fundamental concepts in statistics is the concept of sample mean. Properties of the sample mean that are well-defined in Euclidean spaces become unwieldy or even unclear in graph spaces. Open problems related to the sample mean of graphs include: non-existence, non-uniqueness, statistical inconsistency,…
Somed2Vec learns medical concept embeddings from SNOMED-CT, improving healthcare analytics.
problem Lack of effective vector representations for medical concepts in healthcare analytics.
method Graph-based representation learning using random walks and Poincaré embeddings on SNOMED-CT.
result Concept embeddings from SNOMED-CT significantly outperform state-of-the-art embeddings.
Unsupervised method constructs knowledge graph from text and code.
problem Lack of structured knowledge in scientific literature and code.
method Word embedding, clustering, and dimensionality reduction techniques.
result Enhanced understanding of scientific literature and code.
New method models negative correlations in knowledge graphs.
problem Lack of negative correlation in probabilistic extensions of order embeddings.
method Box lattice measures for probabilistic modeling of negative correlations.
result Models can now capture negative correlations and disjoint concepts.
Generative concept representations improve deep learning by handling uncertainty and integrating learning and reasoning.
problem Discriminative deep learning struggles with uncertainty and lacks integration of learning and reasoning.
method Probabilistic and generative deep learning, variational autoencoders, and generative adversarial networks.
result Generative concept representations enhance deep learning by addressing these limitations.
Study on teaching complexity in graphs, proving hardness and tractability.
problem Computing the minimum number of examples per concept for teaching.
method Classical and parameterized complexity analysis, NP-hardness, upper and lower bounds, fixed-parameter tractability.
result Nearly complete understanding of teaching complexity in graphs.
Study of digital topology concepts like hyperspaces and function graphs.
problem Adapting classical topology concepts to digital topology.
method Define digital hyperspaces and function graphs, study their properties.
result Some relationships and graphical properties of digital hyperspaces and function graphs.
We extend the concepts of trivializing and knotting numbers for knots to spatial graphs and 2-bouquet graphs, in particular. Furthermore, we calculate the trivializing and knotting numbers for projections and pseudodiagrams of 2-bouquet spatial graphs based on the number of precrossings and the placement of the precros…
New clustering methods use motifs to organize networks.
problem Organizing directed graphs efficiently.
method Construct clustering methods parametrized by motifs.
result New clustering methods can organize networks.
Node Masking improves GNNs' scalability and generalization.
problem Improving GNNs' ability to handle arbitrary graphs.
method Introducing Node Masking to enhance GNNs' performance.
result Node Masking enables GNNs to generalize and scale better.
New curvature concept preserves graph distances under operations.
problem Preserving graph distances under graph operations.
method Characterization of distance matrix and its null space.
result Linear system Dx=1 may not have a solution. GCTM integrates GCN into topic models for better topic learning from data streams.
problem Learning hidden topics from short and noisy data streams with concept drift.
method Proposes a graph convolutional topic model (GCTM) that learns from a knowledge graph and old data.
result Significantly better performance in probabilistic predictive measures and topic coherence.
ECG outperforms graph clustering algorithms using ensemble method.
problem Graph clustering challenges.
method ECG combines Louvain algorithm and consensus clustering.
result ECG outperforms leading algorithms on artificial networks.
New methods reduce variance in stochastic computation graph optimization.
problem High variance in gradient estimates from SCGs.
method Introducing value functions, baselines, and critics to derive lower-variance gradient estimates from partial model evaluations.
result Lower-variance gradient estimates from partial model evaluations, making optimization more efficient.
The paper proposes a method to find interpretable subspaces in node embeddings using a knowledge base.
problem Finding interpretable subspaces in unsupervised node embeddings.
method Using a taxonomy of human-understandable concepts from a knowledge base to identify subspaces in node embeddings.
result Low error in finding fine-grained concepts.
NTKs explain GNNs' alignment for graph prediction.
problem Understanding GNNs' alignment for graph prediction.
method Analyzing NTKs and alignment in GNNs, focusing on cross-covariance.
result Optimizing alignment in GNNs optimizes graph representation.
Debias concept-based explanations by removing confounding information.
problem Correlation between concepts and confounding features.
method Causal prior graph and two-stage regression technique.
result Success in removing biases and improving concept ranking.
New method uses CNNs to estimate graph means.
problem Estimating the mean of graph-valued data.
method Convolutional Neural Networks (CNNs) for graph morphology learning.
result CNNs reliably recover the sample Frechet mean.
We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.
Paper proposes a graph network for EHR data that learns robust representations.
problem Learning robust representations for EHR data with implicit connections.
method Variationally regularized encoder-decoder graph network.
result Model outperforms existing methods in various EHR predictive tasks.
A new prior for language concepts inspired by consciousness neuroscience.
problem Learning representations of high-level language concepts.
method Inspired by cognitive neuroscience, a new prior is proposed to help disentangle abstract factors.
result A low-dimensional conscious state can make high-probability statements, consistent with sparse factor graphs.
GRAM addresses healthcare data insufficiency and interpretation challenges using graph-based attention.
problem Data insufficiency and lack of interpretability in healthcare predictive modeling.
method GRAM integrates EHR with medical ontologies, using attention mechanisms to represent medical concepts.
result GRAM outperforms RNN in accuracy and interpretability, using less data.
The aim of the present article is to give an overview of spectral theory on metric graphs guided by spectral geometry on discrete graphs and manifolds. We present the basic concept of metric graphs and natural Laplacians acting on it and explicitly allow infinite graphs. Motivated by the general form of a Laplacian on …
Proposes SimPool for graph pooling using structural similarity features.
problem Challenges in graph pooling due to lack of spatial locality.
method Integrates structural similarity features with a revised pooling layer to propose SimPool.
result SimPool produces node cluster assignments resembling CNN's locality preserving pooling.
Sheaves on graphs link to noncommutative geometry.
problem Exploring noncommutative geometry concepts on graphs.
method Sheaf theory and simplicial sets.
result Enhanced understanding of discrete noncommutative geometry.
We prove surfaces are unknotted with specific properties.
problem Unknottedness of free boundary minimal surfaces and self-shrinkers.
method Introduced concepts of boundary graph and graph at infinity to prove unknottedness.
result Proved surfaces are unknotted with specific properties.
Proves graph 3-manifold groups have two specific properties.
problem Understanding fundamental groups of graph 3-manifolds.
method Constructing sequences of covers to prove properties.
result Graph 3-manifold groups are virtually poly-free and in Lex family.
A new framework forecasts stock trends by mining shared information from concepts.
problem Forecasting stock trends using static concept information limits accuracy.
method Proposes a graph-based framework that mines concept-oriented shared information from both predefined and hidden concepts.
result Improves stock trend forecasting performance through dynamic concept relevance and hidden concept information.
A new clustering algorithm inspired by Wittgenstein's philosophy.
problem Clustering data without assuming predefined cluster shapes or sizes.
method Wittgenstein's family resemblance concept applied to machine learning.
result WFR clustering algorithm effectively identifies clusters in data.
The paper connects graph properties to moral graphs and proves the complexity of deciding morality.
problem Deciding the morality of a graph.
method Defining new graph properties and proving their equivalence to morality, and showing the complexity of the problem.
result Morality can be decided in polynomial time for graphs with maximum degree less than 5, but is NP-complete for higher degrees.
Graph homomorphism numbers embed graphs for classification.
problem Graph classification using graph homomorphisms.
method Embed graphs into vectors using homomorphism numbers.
result Homomorphism vectors are universal for approximating graph invariants.
In this paper, we introduce the concept of the independence graph of a directed 2-complex. We show that the class of diagram groups is closed under graph products over independence graphs of rooted 2-trees. This allows us to show that a diagram group containing all countable diagram groups is a semi-direct product of a…
Image visibility graphs map images into graphs for processing and classification.
problem Mapping image structures into graphs for processing and classification.
method Introduced image visibility graphs (IVGs) and explored their use in image processing and classification.
result IVGs encapsulate relevant image structure information and are computationally efficient.
The pants graph of a free group is constructed and studied.
problem Understanding the structure of free groups through graph theory.
method Developed a pants graph and studied its properties.
result The pants graph of a free group is connected and unbounded.
This thesis explores deep learning on graphs, focusing on encoding and decoding.
problem Deep learning on graph-structured data is underexplored.
method Introduces Edge-Conditioned Convolutions (ECC) for graph encoding and SuperPoint Graph for intermediate representation.
result Developed GraphVAE for generating graphs with variable node counts.
Enhanced spectral clustering for geometric graphs improves clustering accuracy.
problem Ineffective standard spectral clustering for geometric graphs.
method Higher-order spectral clustering using higher-order eigenvectors.
result Established weak and strong consistency for Soft Geometric Block Model.
We extend to dimension n≥3 the concept of ρ-pair in a coloured graph and we prove the existence theorem for minimal rigid crystallizations of handle-free, closed n-manifolds.
The study extends Tutte's conflict graph concept to nonplanar graphs.
problem Understanding the structure of nonplanar graphs through conflict graphs.
method Defining a signed conflict graph for maximally planar subgraphs and analyzing their balance.
result For graphs with a flat embedding, every maximal planar subgraph has unbalanced conflict graphs if and only if the graph is intrinsically linked.