Financial institutions use LSTM models to predict customer goals.
problem Predicting customer goals and actions in financial services.
method Used LSTM models with state-space graph embeddings on historical customer traces.
result Demonstrated the effectiveness of LSTM models in predicting customer goals and actions.
New method learns high-quality Laplacian representations for reinforcement learning.
problem Lack of accurate Laplacian representations in large or continuous state spaces.
method Reformulated spectral graph drawing objective to have eigenvectors as unique global minimizer.
result Learned Laplacian representations more faithfully approximate the ground truth.
This study uses persistent homology to analyze complex transitional networks from time series data.
problem Lack of effective tools to summarize complex topology in transitional networks.
method Persistent homology from topological data analysis applied to coarse-grained state-space networks (CGSSN).
result CGSSN improves dynamic state detection and noise robustness compared to other methods.
Proposes GFMMD for comparing signals on graphs.
problem Computing distances between distributions on graphs.
method Graph Fourier MMD (GFMMD) using optimal witness functions.
result Analytical solution and embedding of distributions.
Federated learning interprets temporal dynamics across clients with graph attention.
problem Interpreting temporal patterns across decentralized, heterogeneous systems with nonlinear dynamics.
method Graph Attention Network for learning state transition models over latent states communicated between clients.
result First interpretable characterization of cross-client temporal interdependencies in decentralized nonlinear systems.
Graph Kalman filters adapt classical filters to graph data.
problem Adapting classical Kalman filters to graph data.
method Generalizes Kalman filters to attributed graphs, learning state-transition and readout functions end-to-end.
result Adapted Kalman filters can predict graph outputs.
We introduce Deep Variational Bayes Filters (DVBF), a new method for unsupervised learning and identification of latent Markovian state space models. Leveraging recent advances in Stochastic Gradient Variational Bayes, DVBF can overcome intractable inference distributions via variational inference. Thus, it can handle …
From social networks to Internet applications, a wide variety of electronic communication tools are producing streams of graph data; where the nodes represent users and the edges represent the contacts between them over time. This has led to an increased interest in mechanisms to model the dynamic structure of time-var…
The goal of this note is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in the larger state space.
We obtain necessary conditions for the existence of complete vertical graphs of constant mean curvature in the Hyperbolic and Steady State spaces. In the two-dimensional case we prove Bernstein-type results in each of these ambient spaces.
A fast graph embedding method for large graphs.
problem Efficiently embedding large graphs for various applications.
method One-hot graph encoder embedding with linear complexity.
result Graph encoder embedding is approximately normally distributed and converges to its mean.
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear coordinate transformations with data-driven methods. Recently, researchers have pro…
Introduces R-SSM for modeling multi-object dynamics with GNNs and normalizing flows.
problem Complex interactions and evolutions in multi-object systems are hard to model.
method Relational state-space model (R-SSM) using graph neural networks (GNNs) and normalizing flows.
result Empirically validated on synthetic and real datasets.
Study of unoriented SL(4) foams in 3-manifolds.
problem Understanding unoriented SL(4) foams in 3-manifolds.
method Combinatorial evaluation and state space study of unoriented SL(4) foams.
result State space of any web is free of rank given by the number of its 4-colorings over a localized ground ring.
Well-quasi-orders proved on embedded planar graphs.
problem Proving well-quasi-orders on embedded planar graphs.
method Careful analysis and extensions of classical methods for embedded minor relations.
result Embedded minor relations are well-quasi-orders on various classes of embedded planar graphs.
Two new methods improve graph embedding without needing a complete graph structure.
problem Graph autoencoders' performance depends on the adjacency matrix quality.
method BAGE and VBAGE: unsupervised graph embedding via adaptive graph learning.
result The methods expand GAEs' applicability to datasets without graph structure.
Curvature regularization prevents distortion in graph embeddings.
problem Graph topology patterns distort in Euclidean space, making detection difficult.
method Proposes curvature regularization to enforce flatness in embedding manifolds.
result Significant improvements in five embedding methods on open graph datasets.
Framework uses RL with dynamic embedding to outperform benchmarks in volatile markets.
problem Challenges in high-dimensional, non-stationary, and noisy market information.
method Dynamic embedding of market information using generative autoencoders and online meta-learning in a reinforcement learning framework.
result Framework outperforms common portfolio benchmarks and PTO approach during market stress.
Paper proposes a novel graph recovery attack from node embeddings.
problem Privacy risks of integrating graph embeddings with machine learning pipelines.
method Model-agnostic graph recovery attack exploiting preserved structural information in node embeddings.
result Adversaries can recover graph edges with decent accuracy from node embeddings alone.
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.
We announce results about flat (linkless) embeddings of graphs in 3-space. A piecewise-linear embedding of a graph in 3-space is called {\it flat} if every circuit of the graph bounds a disk disjoint from the rest of the graph. We have shown: (i) An embedding is flat if and only if the fundamental group of the compleme…
There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedd…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not scale well to large graphs. We therefore propose a framework for parallel computat…
Efficiently computes embeddings for large graphs using coarsening.
problem Inefficient computation of graph embeddings for large-scale graphs.
method Graph coarsening based on Schur complements and Gaussian elimination.
result Efficiently computed embeddings on coarsened graph match Schur complement embeddings in expectation.
A new framework for knowledge graph embedding using sheaves.
problem Learning representations for entities and relations in knowledge graphs.
method Using cellular sheaves to describe knowledge graph embeddings with consistency constraints.
result A generalized framework for reasoning about knowledge graph embedding models.
WEGL embeds graphs in a vector space for faster machine learning.
problem Efficiently embedding graphs for machine learning tasks.
method Wasserstein distance for node embedding similarity, Monge maps for graph representation.
result State-of-the-art classification performance with superior computational efficiency.
Two graph homologies help compute embedding space.
problem Computing the rational homotopy group of long embeddings.
method Invented two graph homologies and constructed a map between them.
result A monomorphism from top hairy graph homology to top BCR graph homology.
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques aim to automatically create a low-dimensional representation of a given graph, whi…
Graphs embeddable on torus and linklessly in 3D can be embedded linklessly in standard torus.
problem Embedding linklessly in a standard torus for graphs embeddable on torus and in 3D.
method Analyzing graphs of order 9 and below, showing linkless embedding in standard torus.
result For graphs of order 9 and below, linkless embedding in standard torus is possible.
Plan2Vec learns image representations without labels, improving control tasks.
problem Learning image representations without labeled data.
method Constructs a weighted graph using near-neighbor distances and extrapolates to global embedding.
result Plan2Vec achieves accurate long-term value estimates in control tasks with reduced computational and memory costs.
New sampling methods improve node embedding efficiency.
problem Efficiency and scalability in node embedding methods.
method Sampling approaches to node embedding, modeling eigenvectors and feature vectors.
result Improved computational efficiency and scalability.
Characterizes graphs with leveled embeddings and introduces new graph invariants.
problem Understanding the properties of leveled embeddings in spatial graphs.
method Characterization of graphs with leveled embeddings, introduction of new invariants.
result Characterization of graphs with low level number and determination of specific invariants for complete graphs and complete bipartite graphs.
Solves Skopenkov's problem on graph embedding criteria.
problem Criteria for toroidal embedding of one-vertex ribbon graphs.
method Analyzes one-vertex ribbon graphs with additional disc structure.
result Provides solutions to Skopenkov's problem.
The study evaluates memory and capacity of graph embedding methods.
problem Assessing the memory and capacity of graph embedding methods.
method Not specified in the abstract provided.
result Not specified in the abstract provided.
Graph embedding leaks sensitive graph properties and subgraphs.
problem Privacy risks in graph embedding sharing.
method Three inference attacks and a defense mechanism.
result High accuracy in inferring graph properties and subgraphs.
Landmark-based node embeddings approximate shortest path distances in random graphs.
problem Capturing global graph distances in node representations.
method Landmark-based node embeddings using shortest path distances from a subset of reference nodes (landmarks).
result Random graphs require lower dimensions in landmark-based embeddings compared to worst-case graphs.
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency structure on the half-edges around each vertex, and an embedding of a *-graph is…
A graph embedded in the 3-sphere is called irreducible if it is non-splittable and for any 2-sphere embedded in the 3-sphere that intersects the graph at one point the graph is contained in one of the 3-balls bounded by the 2-sphere. We show that irreducibility is preserved under certain deformations of embedded graphs…
Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data, but they have mostly ignored the data distribution of the laten…
Paper proposes KE-GCN for better graph embedding.
problem Efficiently leveraging complex graphs with heterogeneous entities and relations.
method Combines GCNs and knowledge embedding methods.
result Advantages in knowledge graph alignment and entity classification.
Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-B…
Enhances graph classification with multiple graphs.
problem Improving graph classification accuracy with multiple graphs.
method Graph fusion embedding using encoder embedding.
result The method consistently improves classification accuracy for large vertex sets.
Graph embedding techniques have been increasingly deployed in a multitude of different applications that involve learning on non-Euclidean data. However, existing graph embedding models either fail to incorporate node attribute information during training or suffer from node attribute noise, which compromises the accur…
With the great success of graph embedding model on both academic and industry area, the robustness of graph embedding against adversarial attack inevitably becomes a central problem in graph learning domain. Regardless of the fruitful progress, most of the current works perform the attack in a white-box fashion: they n…
Algorithm calculates genus of embedded graphs on surfaces.
problem Finding minimal and maximal genus for graph embeddings.
method Constructing special branched coverings of the 2-sphere.
result Algorithm calculates orientable genus and maximal genus of graphs.
Introduces PELP for graph-enhanced word embeddings.
problem Combining graph side-information into static word embeddings.
method Probabilistic embeddings using Laplacian priors.
result Unified and flexible approach to various embedding methods.
Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and visualization. Most existing approaches represent graph nodes as point vectors i…
For leveled spatial graphs, we find a surface embedding that allows cellular embedding.
problem Finding a surface embedding for general spatial graphs is not always possible.
method Define leveled property, decompose graph into subgraphs, and construct surface.
result For leveled spatial graphs with a small number of levels, a surface can always be found.