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.
This paper describes a general framework for learning Higher-Order Network Embeddings (HONE) from graph data based on network motifs. The HONE framework is highly expressive and flexible with many interchangeable components. The experimental results demonstrate the effectiveness of learning higher-order network represe…
A scalable framework preserves personalized higher-order network proximities.
problem Lack of expressive methods to preserve personalized higher-order network proximities.
method Incorporates random walk into a sound objective to preserve arbitrary higher-order proximities and introduces random walk with restart for personalized-weighted preservation.
result Consistently and substantially outperforms state-of-the-art methods on real-world networks.
Study proves higher-order conformal forms don't exist in odd dimensions.
problem Proving non-existence of higher-order conformal forms in odd dimensions.
method Analyzing conformal hypersurface embeddings and differential order invariants.
result General non-existence of higher-order conformal forms in odd dimensions.
HONEM learns embeddings for higher-order networks, improving performance in various tasks.
problem Existing methods fail to capture non-Markovian higher-order dependencies in networks.
method HONEM is a higher-order network embedding method designed for HON, capturing non-Markovian dependencies.
result HONEM outperforms other methods in node classification, network reconstruction, link prediction, and visualization.
GEM improves recommendation by capturing complex feature interactions.
problem Capturing complex high-order interaction signals in feature-based recommendation models.
method Integrates graph convolution networks to generate high-order embeddings and combines with FM-based models.
result Significant improvement in recommendation performance over baselines.
DAOR efficiently embeds graphs without tuning, improving speed and interpretability.
problem Graph embedding limitations in resource usage, interpretability, and parameter dependence.
method DAOR uses community detection to produce robust, interpretable embeddings without manual tuning.
result DAOR outperforms state-of-the-art techniques on node classification and link prediction.
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.
Proposes new embeddings for bipartite graphs to better capture indirect relationships.
problem Typical graph embeddings fail to capture type-specific features in bipartite graphs.
method Develops two types of embeddings (FOBE and HOBE) that decompose edges into indirect relationships and uses algebraic distance for higher-order sampling.
result Ensemble embeddings improve performance over individual methods in link prediction and recommendation tasks.
EPINE enhances network embedding by improving adjacency matrix-based high-order proximity.
problem Inaccurate and poorly designed calculation of high-order proximity in network embedding.
method EPINE redefines high-order proximity intuitively and proposes a scalable algorithm for accurate calculation.
result EPINE outperforms existing methods in network reconstruction, link prediction, and node classification.
A new method learns node embeddings for signed directed networks by capturing both first-order and high-order topologies.
problem Learning representative node embeddings for signed directed networks considering both first-order and high-order topologies.
method Proposes a decoupled variational embedding (DVE) method that leverages a specially designed auto-encoder structure to capture both first-order and high-order topologies.
result Extensive experiments on real-world datasets show the effectiveness of DVE in link sign prediction and node recommendation tasks.
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.
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3,Σ) among all possible embedded closed/bordered surfaces with given geometric/algebraic g…
A new method for embedding sparse high-order interactions.
problem Learning embeddings from sparse high-order interaction events.
method Hybridizing sparse hypergraph and matrix Gaussian processes.
result Strong asymptotic bounds on sparsity ratio.
Recent work in learning ontologies (hierarchical and partially-ordered structures) has leveraged the intrinsic geometry of spaces of learned representations to make predictions that automatically obey complex structural constraints. We explore two extensions of one such model, the order-embedding model for hierarchical…
The study of higher-order homology embeddings for manifold topology.
problem Understanding the structure of higher-order homology embeddings to disclose geometric or topological information.
method Analysis of the null space of the k-th order Laplacian and proposing an algorithm to factorize the homology embedding. result The proposed spectral loop detection algorithm is more efficient and effective on various data types.
Explicit high-order feature interactions efficiently capture essential structural knowledge about the data of interest and have been used for constructing generative models. We present a supervised discriminative High-Order Parametric Embedding (HOPE) approach to data visualization and compression. Compared to deep emb…
Generalizes holographic method to higher codimension submanifolds.
problem Extract higher-order local invariants of embeddings.
method Natural generalization of holographic method to higher codimension submanifolds.
result New invariants obstructing the order-by-order construction of unit defining maps.
Generative Adversarial Network embedding improves network feature representations.
problem Improving low-dimensional feature representations for network applications.
method Adapting Generative Adversarial Network (GAN) to perform network embedding, using cosine similarity, first-order proximity, and second-order proximity.
result GANE-O2 model achieves similar performance to GANE-O1 with simplified training process.
In this paper, we provide some results on Skorokhod embedding with local time and its applications to the robust hedging problem in finance. First we investigate the robust hedging of options depending on the local time by using the recently introduced stochastic control approach, in order to identify the optimal hedgi…
Hermite polynomials improve private data generation by reducing feature count.
problem Infinite-dimensional features in kernel mean embedding are impractical for private data generation.
method Replace random features with Hermite polynomial features, leveraging their ordered nature.
result Hermite polynomial features yield a more accurate approximation of kernel mean embedding with fewer features.
Given a smooth 2-dimensional Riemannian or pseudo-Riemannian manifold (M,g) and an ambient 3-dimensional Riemannian or pseudo-Riemannian manifold (N,h), one can ask under what circumstances does the exterior differential system I for the isometric embedding $M\hookrightarrow …
In order to model entanglements of polymers in a confined region, we consider the linking numbers and writhes of cycles in random linear embeddings of complete graphs in a cube. Our main results are that for a random linear embedding of Kn in a cube, the mean sum of squared linking numbers and the mean sum of square…
A new method for embedding heterogeneous networks using spacey random walks.
problem Stationarity issues in meta-path guided random walks for HIN embedding.
method Heterogeneous personalized spacey random walk.
result Substantial improvement over existing network embedding algorithms.
This paper proposes an out-of-sample extension framework for a global manifold learning algorithm (Isomap) that uses temporal information in out-of-sample points in order to make the embedding more robust to noise and artifacts. Given a set of noise-free training data and its embedding, the proposed framework extends t…
New operators and curvatures derived from embedded manifolds.
problem Finding obstructions and coupling extrinsic operators.
method Explicit computation of extrinsic Paneitz operator and its applications.
result New extrinsically-coupled fourth and sixth order operators.
Paper generalizes wrinkled embedding concept to jet spaces.
problem Approximating homotopies of embeddings with singularities.
method Defines wrinkled embeddings for differential information in jet spaces.
result Holonomic approximation theorem holds for multi-valued sections with simple singularities.
Study proposes an alternative method to measure societal biases using smoothed co-occurrence relations.
problem Measuring societal biases using word embeddings can introduce irrelevant concepts.
method Proposes an alternative approach using smoothed first-order co-occurrence relations.
result First-order approach shows higher correlations with actual gender bias statistics.
Study on topological order on fractal geometries, proving no-go theorem and fault-tolerant gates.
problem Investigating topological order on fractal geometries embedded in n dimensions.
method Using quantum error-correcting codes and systolic geometry to diagnose topological order.
result Proves no-go theorem for topological order on 2D fractals, survival on higher dimensions, and construction of fault-tolerant gates.
Let X be a complex manifold and S↪X be an embedding of complex submanifold. Assuming that the embedding is (k−1)-linearizable or (k−1)-comfortably embedded, we construct via the deformation to the normal cone a diffeomorphism F from a small neighborhood of the zero section in the normal bundle …
Disk Embeddings tackle embedding DAGs with exponential growth.
problem Embedding DAGs with exponentially increasing ancestors and descendants.
method Disk Embeddings framework for quasi-metric spaces, including Hyperbolic Disk Embeddings.
result Disk Embeddings outperform existing methods in complex DAGs.
Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.) and edges characterize the relationships between these primitives. However, these …
TransINT embeds KGs by preserving implication rules, outperforming existing methods.
problem Embedding KGs while preserving relation implications for better access and analysis.
method Isomorphic intersections of linear subspaces with shared parameters for missing facts.
result Significant performance improvement in link prediction and triple classification.
We study the problem of isometrically embedding a two-dimensional Riemannian manifold into Euclidean three-space. It is shown that if Gaussian curvature vanishes to finite order and its zero set consists of two smooth curves tangent at a point, then local sufficiently smooth isometric embedding exists.
We study the old problem of isometrically embedding a 2-dimensional Riemannian manifold into Euclidean 3-space. It is shown that if the Gaussian curvature vanishes to finite order and its zero set consists of two Lipschitz curves intersecting transversely at a point, then local sufficiently smooth isometric embeddings …
Paper reproduces and enhances a method for cross-lingual word embeddings.
problem Creating robust cross-lingual mappings of word embeddings without supervision.
method Reproduces and enhances a self-learning method with grid search for hyperparameters.
result Model's robustness is demonstrated across four new languages.
pLogicNet combines logic rules and embeddings for efficient knowledge graph reasoning.
problem Efficiently predicting missing facts in knowledge graphs.
method Combines Markov Logic Networks with knowledge graph embeddings using variational EM algorithm.
result pLogicNet outperforms traditional methods on multiple knowledge graphs.
Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order word co-occurrence based arrays, or \textit{tensors}. We present four word embedd…
We desingularise the union of 3 Grim paraboloids along Costa-Hoffman-Meeks surfaces in order to obtain complete embedded translating solitons of the mean curvature flow with 3 ends and arbitrary finite genus.
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.
Study non-Abelian gauge theories using Poisson bracket structures.
problem Defining a Poisson bracket structure on solution spaces.
method Using coisotropic embedding theorem.
result Defined Poisson bracket structure for non-Abelian gauge theories.
The universal order 1 invariant f^U of immersions of a closed orientable surface into R^3, whose existence has been established in [N3], takes values in the group G_U = K \oplus Z/2 \oplus Z/2 where K is a countably generated free Abelian group. The projections of f^U to K and to the first and second Z/2 factors are de…
This work improves tensor decomposition methods, especially for large datasets.
problem Lack of efficient methods for estimating Tucker decompositions.
method Applies Johnson-Lindenstrauss type guarantees to Tucker decompositions with random embeddings.
result Effective dimension reduction with minimal error for large tensors.
Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.
problem Establishing inequalities for radial functions on hyperbolic spaces without zero boundary conditions.
method Novel approach considering both bounded and unbounded domains, focusing on weighted Sobolev and Adams-Trudinger-Moser embeddings.
result Theorems 1.2, 1.3, and 1.4 for weighted Sobolev embedding theorems, and Theorems 1.5 and 1.6 for Adams-Trudinger-Moser type embedding theorems.
In a spatially embedded network, that is a network where nodes can be uniquely determined in a system of coordinates, links' weights might be affected by metric distances coupling every pair of nodes (dyads). In order to assess to what extent metric distances affect relationships (link's weights) in a spatially embedde…
LATTE tackles heterogeneous network embedding challenges with layer-stacked attention.
problem Aggregating higher-order indirect relations in heterogeneous networks.
method Layer-stacked ATTention Embedding (LATTE) that decomposes meta relations at each layer.
result LATTE achieves state-of-the-art performance on benchmark datasets.
Enhances image classification by integrating semantic hierarchy into CNN models.
problem Limited use of external guidance in image classification.
method Integrates label-hierarchy knowledge into CNN-based classifiers and uses order-preserving embeddings.
result Boosts image classification performance through semantic hierarchy integration.
A proof of the isometric embedding of a given two-metric in E^3 of class C^1. The method uses the theory of first order partial differential equations. The curvature of the metric plays no role in the proof.