Proposes cone embedding for better graph hierarchical structure representation.
problem Lack of natural and interpretable hierarchical indicators in graph embeddings.
method Metric cone embedding method to capture hierarchical structure.
result Extracts hierarchical structure from other graph embedding outputs.
Paper explores duality in DPPs using embedding structure analysis.
problem Understanding the geometric structure of determinantal point processes.
method Analyzes the exponential family embedding of DPPs and uses the e-embedding curvature tensor.
result Discovers the duality between marginal and L-ensemble kernels.
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.
The abstract discusses embedding manifolds in open books and contact structures.
problem Embedding manifolds in open books and contact structures.
method Using open book embeddings and contact structures, the abstract proves embedding theorems for various manifolds.
result Closed manifolds can be embedded in open books and contact structures.
The paper explores theories behind graph and relational data vector embeddings.
problem Understanding the foundations of vector embeddings for graphs and relational structures.
method Proposes two theoretical approaches to understand vector embeddings.
result Draws connections between various embedding techniques and suggests future research directions.
Paper shows graphs can be embedded in lower dimensions than expected.
problem Choosing the right embedding dimension for graph analysis.
method Utilizes hidden manifold structure to predict lower-dimensional embedding.
result Graphs can be embedded in much lower dimensions than previously thought.
This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that the relationship between structural representations and node embeddings is analogo…
Any Sasakian structure can be closely mimicked by embeddings into weighted spheres.
problem Approximating Sasakian structures on closed manifolds.
method Using CR embeddings into weighted Sasakian spheres and strengthening previous approximation results.
result Sasakian structures can be approximated in the Cq-norm by embeddings into weighted Sasakian spheres. We reduce the embedding problem for hypo SU(2) and SU(3)-structures to the embedding problem for hypo G2-structures into parallel Spin(7)-manifolds. The latter will be described in terms of gauge deformations. This description involves the intrinsic torsion of the initial G2-structure and allows us to prove that the ev…
CR embeddings in complex spaces for specific Lie groups.
problem Embedding specific Lie groups in complex spaces.
method Using integrable complex structures on subbundles of tangent bundles.
result CR embeddings possible as the edge of wedges in complex domains.
New method learns output embeddings for structured prediction.
problem Structured prediction with output embeddings.
method Jointly learns output embedding and regression function.
result Structured predictor is a consistent estimator with smaller complexity.
The paper explores how semantic independence can be captured in text embeddings using partial orthogonality.
problem Capturing semantic independence in text embeddings.
method Developed a theory and methods based on partial orthogonality to demonstrate semantic independence.
result Partial orthogonality captures semantic independence in text embeddings.
Normal forms and isotropic embeddings via Euler-like vector fields.
problem Proving normal forms results for geometric structures.
method Construction of Euler-like vector fields compatible with geometric structures.
result Illustrated in various examples, including Morse-Bott, Weinstein, and Zung's theorems.
This work benchmarks neural embeddings for link prediction in evolving knowledge graphs.
problem Evaluating the robustness of neural embeddings in changing knowledge graphs.
method Proposes an open-source evaluation pipeline using relation-centric connectivity measures.
result Demonstrates the importance of simulating embedding accuracy for frequently updated knowledge graphs.
Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete probability distributions in a Wasserstein space, endowed with an optimal transport metri…
Textual network embedding aims to learn low-dimensional representations of text-annotated nodes in a graph. Prior work in this area has typically focused on fixed graph structures; however, real-world networks are often dynamic. We address this challenge with a novel end-to-end node-embedding model, called Dynamic Embe…
This paper introduces an acceleration structure for hyperbolic embeddings.
problem Efficiently embedding and visualizing high-dimensional data in hyperbolic spaces.
method Building upon a polar quadtree, the paper introduces a new acceleration structure for hyperbolic embeddings.
result The new method computes embeddings in significantly less time compared to existing methods.
LASE improves local network structure visualization by targeting locally low-dimensional regions.
problem Global spectral embedding fails to capture local geometric features in sparse, transitive networks.
method Local Adjacency Spectral Embedding (LASE) using weighted spectral decomposition.
result LASE reveals locally low-dimensional structure, improving local reconstruction and visualization.
PGEL learns embeddings to diversify protein motifs while maintaining biological function.
problem Generating diverse protein structures while preserving biological function.
method Embedding learning framework that enhances motif diversity in a diffusion model's frozen denoiser.
result PGEL achieves greater structural diversity, better designability, and improved self-consistency compared to partial diffusion.
This paper solves PDEs for embedding discrete lattices into smooth manifolds.
problem Embedding discrete lattices into smooth manifolds while preserving geometric and topological properties.
method Rigorous mathematical framework and analysis of partial differential equations (PDEs).
result Existence and regularity of solutions to PDEs under initial boundary conditions.
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…
A framework for stable dynamic network embeddings using static methods.
problem Dynamic network embedding in a nascent field.
method Using static network embedding methods on dilated unfolded adjacency matrices.
result Stable embeddings that preserve latent node behavior across time.
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.
The paper extends a link criterion for Lipschitz normal embeddings to definable sets in o-minimal structures.
problem Characterizing Lipschitz normal embeddings of definable sets.
method Extending a known result about subanalytic germs to definable germs in any o-minimal structure.
result The link criterion holds for definable germs in o-minimal structures, but is not sufficient for all homomorphisms.
DeepWalk embeddings converge on SBM graphs, recovering cluster structure.
problem Theoretical guarantees for DeepWalk embeddings on complex graphs.
method Solving a nonconvex optimization problem using random walks.
result DeepWalk embeddings on SBM graphs recover cluster structure with high probability.
The creation of social ties is largely determined by the entangled effects of people's similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making it difficult to determine which has greater responsibility in the formation of t…
New embeddings capture local structure in complex networks.
problem Embeddings cannot capture local structure in complex networks.
method Logistic Principal Component Analysis (LPCA) algorithm for exact low-rank representations.
result Exact low-rank representations of real-world networks are possible.
IDGL learns better graph structure and embeddings iteratively.
problem Improving graph neural network node embeddings and graph structure.
method Iterative Deep Graph Learning framework that dynamically stops when graph structure optimizes for downstream tasks.
result IDGL consistently outperforms state-of-the-art baselines on nine benchmarks.
Unified Lie structures in homotopy and isotopy calculus.
problem Compatibility of Lie structures in homotopy and isotopy calculus.
method New technical tool: bracket on total homotopy fibres of collapsing cubes of wedge sums.
result Unified understanding of Lie structures in homotopy and isotopy calculus.
Generates low-dimensional node vectors for graphs with privacy while preserving structural preferences.
problem Publishing graph node vectors can leak sensitive individual information.
method SE-PrivGEmb, a skip-gram based technique with a unified noise tolerance mechanism and negative sampling probabilities.
result Our method outperforms existing methods in structural equivalence and link prediction tasks.
New methods explain NE embeddings by identifying key variables.
problem Lack of interpretability in NE techniques.
method Combining PCA, Q-residuals, Hotelling's T2, and visualization.
result Identifies discriminatory features not seen in standard approaches.
Paper presents a new method for learning hyperbolic representations using tree structures.
problem Learning faithful low-dimensional hyperbolic embeddings of data.
method Metric-first approach to learn tree structure, then embed into hyperbolic manifold.
result Novel fast algorithm TreeRep learns tree approximating original metric.
Proposes Gromov-Wasserstein methods for multi-view embedding.
problem Integrating multiple representations of the same samples in heterogeneous geometries.
method Gromov-Wasserstein optimal transport for multi-view embedding.
result Preserves intrinsic relational structure across views effectively.
Inferring the structural properties of a protein from its amino acid sequence is a challenging yet important problem in biology. Structures are not known for the vast majority of protein sequences, but structure is critical for understanding function. Existing approaches for detecting structural similarity between prot…
CTGCN learns dynamic graph embeddings preserving both local and global graph structure.
problem Learning node representations for evolving graphs while preserving both local and global graph structure.
method CTGCN uses k-core based temporal graph convolutional network to learn dynamic graph embeddings.
result CTGCN outperforms existing methods in link prediction and structural role classification.
DiSeNE generates interpretable node embeddings without supervision.
problem Lack of interpretability in unsupervised node embeddings.
method Disentangled representation learning with novel objective functions and metrics.
result DiSeNE produces interpretable node embeddings aligned with graph structure.
Network embedding represents nodes in a continuous vector space and preserves structure information from the Network. Existing methods usually adopt a "one-size-fits-all" approach when concerning multi-scale structure information, such as first- and second-order proximity of nodes, ignoring the fact that different scal…
The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when the projection operator achieves a stable embedding of the data by satisfying th…
Most of existing manifold learning methods rely on Mean Squared Error (MSE) or ℓ2 norm. However, for the problem of image quality assessment, these are not promising measure. In this paper, we introduce the concept of an image structure manifold which captures image structure features and discriminates image dist…
This paper studies node embeddings of networks, revealing their geometric properties.
problem Understanding the geometric properties of node embeddings in random networks.
method Characterization of ergodic limits, generalization, and convex relaxations of random walk node embedding objectives.
result The optimal node embedding Grammians have rank 1 for a nuclear norm relaxation of the non-randomized objective.
Graph embedding method captures both local and global network structure.
problem Representing and analyzing complex graph networks.
method Spectral embedding based on a generalized graph Laplacian.
result Significant improvement in data analysis tasks.
PIF detects anomalies in structured patterns using preference embedding.
problem Detecting anomalies with respect to structured patterns.
method PIF combines adaptive isolation methods with preference embedding to compute anomaly scores using a tree-based method, PI-Forest.
result PIF outperforms state-of-the-art techniques in anomaly detection.
NNLMs optimize poorly for word probabilities due to embedding space structure.
problem NNLMs assign suboptimal probabilities to some words.
method Analyzed the inductive bias of NNLMs and the structure of word embeddings.
result Words on the convex hull have bounded probability, affecting others.
The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural information about data. However, recently there has been a surge in approaches that learn …
Study of pseudoconvex 3-manifolds in complex surfaces.
problem Understanding pseudoconvex 3-manifolds in complex surfaces.
method Develop tools for constructing topologically pseudoconvex embeddings and classify almost-complex structures.
result Every closed, oriented 3-manifold can be embedded in a compact complex surface realizing any homotopy class of almost-complex structures.
A new method for efficient structural node embeddings using Von Neumann entropy.
problem Efficiently identifying structurally equivalent nodes in complex networks.
method VNEstruct: a simple approach generating low-dimensional structural node embeddings using Von Neumann entropy.
result VNEstruct achieves robustness on structural role identification and state-of-the-art performance on graph classification tasks.
A new drug embedding method using hierarchical drug relations and chemical structures.
problem Learning accurate drug representations from chemical structures and hierarchies.
method Semi-supervised drug embedding using VAE in hyperbolic space.
result The method accurately places drugs in a hierarchy and predicts side-effects.
A deep learning model organizes RNA graphs to reveal folding patterns and properties.
problem Organizing and understanding the complex folding patterns of RNA secondary structures.
method Geometric scattering autoencoder (GSAE) network for learning graph embeddings.
result GSAE accurately reflects bistable RNA structures and can sample new folding trajectories.