New modularity function improves clustering of spatially embedded networks.
problem Improving clustering in spatially embedded networks for unsupervised learning.
method Developed a new modularity function and compared its performance with existing methods.
result Our modularity function outperforms existing methods in partitioning 2D and 3D granular assemblies.
GSNE improves house price predictions by embedding geo-spatial context.
problem Lack of contextual information in house price prediction models.
method Geo-Spatial Network Embedding (GSNE) using graph neural networks.
result GSNE embeddings consistently improve house price prediction performance.
Proposes flexible spatial models for better understanding spatial heterogeneity.
problem Poor characterisation of spatial heterogeneity in conventional models.
method Spatial Bayesian Neural Networks (SBNNs) incorporating a spatial embedding layer and possibly spatially-varying parameters.
result SBNNs better match the finite-dimensional distribution of target spatial processes.
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…
SCNode improves node embeddings for GNNs in both homophilic and heterophilic graphs.
problem Challenges in node representation quality and generalization in GNNs, especially in heterophilic graphs.
method SCNode integrates spatial and contextual information to create more discriminative and structurally aware node embeddings.
result SCNode achieves superior performance over conventional GNN models on benchmark datasets.
SXL embeds spatial autocorrelation into neural networks for better geographic data learning.
problem Difficulties in learning spatial effects for neural networks in geographic data.
method SXL uses auxiliary tasks and autoregressive embeddings to learn spatial autocorrelation.
result SXL improves neural network training in unsupervised and supervised learning tasks.
A framework converts spatial data into embeddings for insurance risk modelling.
problem Improving underwriting precision and risk management in insurance with spatial data.
method Multi-view contrastive learning framework for generating spatial embeddings.
result Spatial embeddings consistently improve predictive accuracy across various models.
Road networks are a type of spatial network, where edges may be associated with qualitative information such as road type and speed limit. Unfortunately, such information is often incomplete; for instance, OpenStreetMap only has speed limits for 13% of all Danish road segments. This is problematic for analysis tasks th…
A2-SBNN models spatial data with copulas for non-Gaussian dependencies.
problem Capturing complex spatial relationships and extreme dependencies in non-Gaussian data.
method Embedding A2 copula into a Bayesian neural network, trained with Wasserstein loss and moment matching.
result A2-SBNN consistently delivers high accuracy across various dependency strengths.
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.
Study uses trajectory embedding to measure place function similarity at fine spatial granularity.
problem Measuring place function similarity at fine spatial granularity.
method Trajectory embedding to reduce dimensions and measure similarity of place functions.
result Embedding similarity can be a metric proxy for place functions at fine spatial granularity.
Spatial embeddings of planar graphs can have higher unknotting numbers than crossing numbers.
problem Understanding the relationship between unknotting numbers and crossing numbers of spatial embeddings of planar graphs.
method Analyzing specific examples of planar graphs and their spatial embeddings to find counterexamples.
result There exist planar graphs and their spatial embeddings where the unknotting number is greater than half the crossing number.
In this paper, we propose a new pooling method called spatial pyramid encoding (SPE) to generate speaker embeddings for text-independent speaker verification. We first partition the output feature maps from a deep residual network (ResNet) into increasingly fine sub-regions and extract speaker embeddings from each sub-…
We say that a graph is intrinsically non-trivial if every spatial embedding of the graph contains a non-trivial spatial subgraph. We prove that an intrinsically non-trivial graph is intrinsically linked, namely every spatial embedding of the graph contains a non-splittable 2-component link. We also show that there exis…
Neural networks improve geospatial data analysis by relaxing linearity assumptions.
problem Traditional geospatial analysis assumes linear models, limiting flexibility.
method Embedding neural networks within traditional geostatistical models for non-linear mean functions.
result NN-GLS algorithm provides consistent and scalable predictions for irregular spatial data.
DeepKriging uses DNNs to predict spatial data with improved accuracy and scalability.
problem Predicting spatial processes with non-linear and non-Gaussian data.
method Adds an embedding layer of spatial coordinates with basis functions to DNNs.
result DeepKriging provides non-linear predictions with smaller approximation errors and is scalable for large datasets.
SE-KGE embeds spatial data into KGs for better spatial reasoning.
problem Spatially explicit KG embeddings for geographic tasks.
method Location-aware KG embedding model SE-KGE.
result SE-KGE outperforms baselines on DBGeo dataset.
In this paper we construct some invariants of spatial graphs by disk-summing the constituent knots and show the delta edge-homotopy invariance of them. As an application, we show that there exist infinitely many slice spatial embeddings of a planar graph up to delta edge-homotopy, and there exist infinitely many bounda…
Forecasting the future traffic flow distribution in an area is an important issue for traffic management in an intelligent transportation system. The key challenge of traffic prediction is to capture spatial and temporal relations between future traffic flows and historical traffic due to highly dynamical patterns of h…
Calendar graph neural networks model user behavior with location and time data.
problem Modeling user behavior with location and time information for demographic prediction.
method Graph neural networks with a tripartite network of items, sessions, and locations, and a hierarchical calendar network.
result User embeddings preserve spatial and temporal patterns of various periodicity.
Paper presents a method for geographic ratemaking using spatial embeddings.
problem Lack of historical loss data in areas with high exposures.
method Construct spatial features within a complex representation model and use them as inputs to a predictive model.
result Predictions have smaller bias and variance than other spatial interpolation models.
DNNs improve SIMP method but not spatially invariant, study shows.
problem Improving SIMP method with DNNs but maintaining spatial invariance.
method Use of DNNs for density field generation, study of NTK filter properties.
result DNNs lead to a non-spatially invariant filter, requiring embeddings for spatial invariance.
Model traffic congestion events using multi-modal data and attention-based neural networks.
problem Capture non-homogeneous temporal and directional spatial dependencies in traffic congestion events.
method Attention-based neural networks for point processes, adapted tail-up model for spatial statistics.
result Superior performance compared to state-of-the-art methods on synthetic and real data.
Model place cells as spatial embeddings for efficient path planning and cognitive map construction.
problem Encoding spatial navigation in the hippocampus.
method Model place cells using spectral decomposition of multi-step random walk transition kernels, inducing sparsity and adjacency.
result Place cells encode spatial information through non-negativity and inner-product structure, forming a cognitive map.
New method to classify simple Smale flows on S3.
problem Classifying simple Smale flows on S3. method Embedded template and Kauffman's invariant of spatial graphs.
result Isotopic classification of simple Smale flows on S3. Two natural generalizations of knot theory are the study of spatially embedded graphs, and Kauffman's theory of virtual knots. In this paper we combine these approaches to begin the study of virtual spatial graphs.
SX-GeoTree improves spatially coherent explanations in geospatial regression trees.
problem Capturing spatial dependence and producing robust explanations in tabular prediction models.
method Integrates three objectives: impurity reduction, spatial residual control, and explanation robustness via modularity maximization on a consensus similarity network.
result Improves residual spatial evenness and doubles attribution consensus (modularity: Fujian 0.19 vs 0.09; Seattle 0.10 vs 0.05).
Modern navigation services often provide multiple paths connecting the same source and destination for users to select. Hence, ranking such paths becomes increasingly important, which directly affects the service quality. We present PathRank, a data-driven framework for ranking paths based on historical trajectories us…
Neural Spacetimes learn DAGs by embedding nodes in a spacetime manifold.
problem Learning representations of weighted directed acyclic graphs (DAGs).
method Trainable deep learning-based geometries (Neural Spacetimes) that encode both edge weights and causality.
result Universal embedding theorem for DAGs with sub-cubic parameters and low distortion.
Proposes a new model to predict travel demand with zero-inflated and long-tail characteristics.
problem Sparse and long-tailed travel demand data with many zeros.
method Spatial-Temporal Tweedie Graph Neural Network (STTD) using Tweedie distribution.
result STTD provides accurate predictions and precise confidence intervals.
Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the underlying relation between entities is pre-determined. However, the explicit graph…
We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting thr…
This work proposes a novel autoencoder for fusing visible and infrared images.
problem Challenging task to combine spatial and spectral information from visible and infrared images.
method Spatially constrained adversarial autoencoder with residual architecture and adversarial regularizer.
result Generates a more realistic fused image with enhanced spatial and spectral information.
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.
Proves minimal crossing diagrams for specific spatial graphs.
problem Proving minimal crossing diagrams for spatial graphs.
method Analyzing adequate diagrams and replacing vertices and edges.
result All 1-vertex spatial graphs with adequate diagrams have minimal crossing number.
New proof shows no flat embedding for Petersen family graphs.
problem Proving Petersen family graphs have no flat embeddings.
method Applying Böhme's Lemma and the Jordan-Brouwer Separation Theorem.
result Every Petersen family graph has no flat embedding.
The paper introduces groupoid racks for spatial surfaces.
problem Coloring diagrams of spatial surfaces for invariant calculation.
method Introduces groupoid racks with universal properties.
result Groupoid racks provide an invariant for spatial surfaces.
A site-specific Gordian distance between two spatial embeddings of an abstract graph is the minimal number of crossing changes from one to another where each crossing change is performed between two previously specified abstract edges of the graph. It is infinite in some cases. We determine the site-specific Gordian di…
Proposes bivariate DeepKriging for efficient wind field prediction.
problem Challenges in predicting large-scale bivariate wind fields with high spatial variability and heterogeneity.
method Spatially dependent deep neural network (DNN) with embedding layer using spatial radial basis functions.
result Outperforms traditional cokriging predictors and reduces computation time.
A spatial surface is a compact surface embedded in the 3-sphere. In this paper, we provide several typical examples of spatial surfaces and construct a coloring invariant to distinguish them. The coloring is defined by using a multiple group rack, which is a rack version of a multiple conjugation quandle.
Graph embeddings from commute networks identify socioeconomic disparities in urban areas.
problem Urban delineation and socioeconomic group identification.
method Graph Neural Network (GNN) for modeling commute networks and deriving node embeddings.
result GNNs effectively capture socioeconomic disparities between urban communities.
Model predicts unseen climate extremes to inform risk planning.
problem Missing unseen climate extremes in historical records.
method DeepX-GAN model capturing spatial dependence.
result Unseen heat extremes disproportionately threaten vulnerable regions.
We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing number of embedded graphs.
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to spatial point processes. While the original embedding is infinite-dimensional a…
We consider the group of isotopy classes of automorphisms of the 3-sphere that preserve a spatial graph or a handlebody-knot embedded in it. We prove that the group is finitely presented for an arbitrary spatial graph or a reducible handlebody-knot of genus two. We also prove that the groups for "most" irreducible genu…
Study on spatial graphs and their constituent knots, linking polynomial invariants.
problem Understanding the polynomial invariants of spatial graphs and their constituent knots.
method Analyzing spatial K4 graphs, constructing band surfaces, and relating polynomials. result Relations between Yamada/Jaeger polynomials and Jones polynomials of constituent knots and associated links.
The spatial convolution layer which is widely used in the Graph Neural Networks (GNNs) aggregates the feature vector of each node with the feature vectors of its neighboring nodes. The GNN is not aware of the locations of the nodes in the global structure of the graph and when the local structures corresponding to diff…
Extends knotoid theory to include multiple poles and intervals.
problem No new problem introduced.
method Definition of generalized knotoids and graphs, exploration of invariants.
result Theory subsumes various topological objects and introduces new cases.