Structural identity is a concept of symmetry in which network nodes are identified according to the network structure and their relationship to other nodes. Structural identity has been studied in theory and practice over the past decades, but only recently has it been addressed with representational learning technique…
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48 results for “Node Identity”
Augments GNNs with diversification to preserve node identity.
problem Current GNNs filter node information, potentially losing node identity.
method Integrates diversification operators with aggregation to enrich node representations.
result Significant performance boost on 9 node classification tasks.
Graphs (networks) are ubiquitous and allow us to model entities (nodes) and the dependencies (edges) between them. Learning a useful feature representation from graph data lies at the heart and success of many machine learning tasks such as classification, anomaly detection, link prediction, among many others. Many exi…
Study finds significant instability in node embeddings due to randomness.
problem Stability of node embeddings under random variations.
method Evaluated five node embedding algorithms (HOPE, LINE, node2vec, SDNE, GraphSAGE) on synthetic and empirical graphs.
result Significant instability in embedding spaces and downstream task accuracy.
CAWs learn temporal network dynamics without node identities or edge attributes.
problem Learning temporal network dynamics without node identities or edge attributes.
method Causal Anonymous Walks (CAWs) using temporal random walks and hitting counts.
result CAW-N outperforms previous methods in predicting links over 6 real temporal networks.
New decentralized KRR algorithm adapts to node-specific data.
problem Consistent node-specific data in decentralized KRR.
method Data-dependent random features for adaptive RF generation.
result Average regression accuracy improved by 25.5% across six datasets.
GDA-HIN adapts across heterogeneous networks by aligning shared and private node types.
problem Domain adaptation challenges in heterogeneous networks with shared and private node types.
method Generalized Domain Adaptive model across HINs (GDA-HIN) that aligns identical-type nodes and edges while utilizing different-type nodes and edges.
result GDA-HIN outperforms state-of-the-art methods in various domain adaptation tasks across heterogeneous networks.
In this paper, we show that a simple coloring scheme can improve, both theoretically and empirically, the expressive power of Message Passing Neural Networks(MPNNs). More specifically, we introduce a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate identical node att…
GCNIII combines Wide & Deep for better node classification.
problem Issues with graph convolutional networks in node classification tasks.
method Proposes GCNIII framework integrating Wide & Deep architecture and three techniques.
result Demonstrates improved performance in various node classification tasks.
Wide neural networks with asymmetrical node scaling converge globally and learn features.
problem Global convergence and feature learning in over-parameterised shallow networks.
method Gradient-based optimisation of wide, shallow neural networks with asymmetrical node scaling.
result Gradient flow and gradient descent converge to a global minimum and learn features, unlike in the NTK parameterisation.
It is often stated in papers tackling the task of inferring Bayesian network structures from data that there are these two distinct approaches: (i) Apply conditional independence tests when testing for the presence or otherwise of edges; (ii) Search the model space using a scoring metric. Here I argue that for complete…
Node harveststat.ML
When choosing a suitable technique for regression and classification with multivariate predictor variables, one is often faced with a tradeoff between interpretability and high predictive accuracy. To give a classical example, classification and regression trees are easy to understand and interpret. Tree ensembles like…
In this paper, we formulate and prove a general compactness theorem for harmonic maps using Deligne-Mumford moduli space and families of curves. The main theorem shows that given a sequence of harmonic maps over a sequence of complex curves, there is a family of curves and a subsequence such that both the domains and t…
Graph neural networks struggle with structural noise.
problem Robustness of graph neural networks to structural noise.
method Controlled experiments with a representative GNN model.
result Graph neural networks are not robust to structural noise.
In this paper, we study the convergence of Yang-Mills-Higgs fields defined on fiber bundles over Riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the Riemann surface is allowed to vary. We show that away from the nodes, the YMH fields converges, up to gauge, to a smooth Y…
We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized energy identity in the case that the domain converges to a spin surface with only Neveu-Schwarz type nodes. We find condition that is both necessary and sufficient for the …
Method detects anomalies on attributed graphs with few labeled instances.
problem Detecting anomalies on connected instances (attributed graphs) with limited labeled data.
method Embed nodes in latent space using GCNs, training to distinguish normal and anomalous nodes.
result Method outperforms existing methods on real-world attributed graph datasets.
Random walks are at the heart of many existing deep learning algorithms for graph data. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to transfer to new nodes and graphs as they are tied to node identity. In this work, …
Distributed model training is vulnerable to byzantine system failures and adversarial compute nodes, i.e., nodes that use malicious updates to corrupt the global model stored at a parameter server (PS). To guarantee some form of robustness, recent work suggests using variants of the geometric median as an aggregation r…
Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theo…
Distance Encoding: Design Provably More Powerful Neural Networks for Graph Representation Learningcs.LG
DE improves GNNs by distinguishing graph substructures, enhancing accuracy.
problem Limited expressive power of GNNs in representing graph substructures.
method Introduces Distance Encoding (DE) to assist GNNs in distinguishing graph substructures.
result DE distinguishes graph substructures that traditional GNNs cannot, improving accuracy.
A new GNN framework for graphs with heterophily.
problem Graphs with heterophily (nodes from different classes often connected).
method CPGNN framework with an interpretable compatibility matrix.
result CPGNN achieves state-of-the-art results in heterophily settings.
The paper presents efficient methods for identifying causal graphs with latent variables.
problem Recovering causal graphs with latent variables while minimizing intervention costs.
method Two intervention cost models (linear and identity) are considered. Algorithms are provided for both models.
result Upper bounds on the number of interventions needed for recovery, and approximation factors for the linear cost model.
Paper uses SSC for identifying layers with identical community structures in DIMPLE networks.
problem Identifying layers with identical community structures in DIMPLE networks.
method Sparse Subspace Clustering (SSC) for identifying groups of layers with identical community structures.
result SSC leads to strongly consistent between-layer clustering under mild conditions.
SIMPLE-RC method tests group membership profiles in large networks with weak signals.
problem Testing group membership profiles in large networks with weak signals.
method Random coupling technique to construct maximum SIMPLE tests for subsampled node pairs.
result Asymptotic distributions of SIMPLE-RC test are derived, enabling delicate analysis.
Random walks are at the heart of many existing network embedding methods. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to transfer to new nodes and graphs as they are tied to vertex identity. In this work, we introduce…
A critical part of multi-person multi-camera tracking is person re-identification (re-ID) algorithm, which recognizes and retains identities of all detected unknown people throughout the video stream. Many re-ID algorithms today exemplify state of the art results, but not much work has been done to explore the deployme…
We consider the problem of estimating the underlying graph associated with a Markov random field, with the added twist that the decoding algorithm can iteratively choose which subsets of nodes to sample based on the previous samples, resulting in an active learning setting. Considering both Ising and Gaussian models, w…
Optimizes state monitoring in Markovian systems with cost constraints.
problem Balancing state queries with prediction costs in Markovian systems.
method Greedy policy and SGD-based learning variant for optimal predict-query tradeoff.
result Greedy policy is suboptimal but performs close to optimal under certain conditions.
Improves hypergraph link prediction by breaking symmetry.
problem Limited expressivity of GWL-1 algorithm in hypergraph link prediction.
method Preprocessing algorithm to identify and replace symmetry-inducing subhypergraphs with covering hyperedges.
result Improves expressivity of GWL-1, leading to better link prediction.
We present our ongoing work on understanding the limitations of graph convolutional networks (GCNs) as well as our work on generalizations of graph convolutions for representing more complex node attribute dependencies. Based on an analysis of GCNs with the help of the corresponding computation graphs, we propose a gen…
A motif-based framework identifies local spillover structures in financial markets.
problem Aggregate risk spillovers obscure local interaction patterns in systemic risk.
method Develops a motif-based framework using multiscale backbones and colored motifs.
result Motif-based portfolios outperform traditional benchmarks on risk-adjusted returns.
In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum probability of connections between any pair of nodes. As a result, sparsity describes o…
In this paper, we propose a distributed algorithm for stochastic smooth, non-convex optimization. We assume a worker-server architecture where nodes, each having (potentially infinite) number of samples, collaborate with the help of a central server to perform the optimization task. The global objective is to m…
A new test detects noise in graph data, useful for forecasting.
problem Detecting uncorrelated noise in graph data.
method Spatio-temporal extension of traditional tests, using graph signals.
result Asymptotic distribution known, no assumption of identically distributed data.
A framework for large-scale federated learning with non-IID data.
problem Stability of models trained on non-IID data in federated learning.
method Generation of non-IID datasets and modular evaluation framework.
result Open-source benchmark for large-scale federated learning research.
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.
This paper discovers new identities linking geodesic and orthogeodesic lengths on hyperbolic surfaces.
problem Understanding relationships between geodesic and orthogeodesic lengths on hyperbolic surfaces.
method Investigates a broad family of identities involving lengths of all closed geodesics and orthogeodesics.
result Introduces new identities that include lengths of all closed geodesics, contrasting with previous identities.
Establishes a correspondence between two mathematical identities.
problem None explicitly stated; focuses on identity correspondence.
method Establishes correspondence between Pestov and Weitzenböck identities.
result Established correspondence between Pestov and Weitzenböck identities.
This paper explores SSL for graph neural networks, improving performance on real-world datasets.
problem Leveraging unlabeled data for graph neural networks to improve deep learning performance.
method Empirical study of various SSL pretext tasks on graphs and proposing a new approach called SelfTask.
result Proposes SelfTask, achieving state-of-the-art performance on real-world datasets.
New algorithm speeds up causal discovery for network data.
problem Scalability issues in score-matching for temporal network data.
method Developed a new parent-finding subroutine for DAGs, improving score matching efficiency.
result Efficiency-lifted score matching for both i.i.d. and temporal data on networks.
Quandle homology was defined from rack homology as the quotient by a subcomplex corresponding to the idempotency, for invariance under the type I Reidemeister move. Similar subcomplexes have been considered for various identities of racks and moves on diagrams. We observe common aspects of these identities and subcompl…
The paper derives curvature identities for 5D and 6D Einstein manifolds.
problem Deriving curvature identities for specific dimensions of Einstein manifolds.
method Using Patterson's curvature identities and the Chern-Gauss-Bonnet Theorem, the paper provides explicit formulae for 5D and 6D Einstein manifolds.
result The curvature identities for 5D and 6D Einstein manifolds are confirmed to be consistent with previous work.
Global Pestov identity proved on frame bundle and related fibrations.
problem Global Pestov identity on frame bundles and fibrations.
method Global Pestov identity on frame bundles and fibrations.
result Global Pestov identity on frame bundles and fibrations.
Bochner's Identity on Graphsmath.DG
Proves Bochner's identity on graphs using a new auxiliary graph.
problem Extending Bochner's identity to graph theory.
method Introduces a complete tangent graph to prove the identity.
result Validates Bochner's identity on graphs.
Doodles link to commutator identities in a 2-sphere.
problem Understanding commutator identities in free groups via doodles.
method Analyzing doodles with proper noose systems and establishing bijections.
result A bijection between doodles and commutator identities.
The paper studies harmonic identity maps on Riemannian manifolds.
problem Understanding harmonicity of identity maps on Riemannian manifolds.
method Constructing new examples and defining a symmetric tensor field.
result New examples of identity harmonic maps are constructed.
Paper proposes a distributed method to estimate principal eigenvector from high-rate streaming data.
problem Estimating principal eigenvector from high streaming data rate.
method Distributed Krasulina (D-Krasulina) and mini-batch extension (DM-Krasulina) methods.
result Achieves optimal estimation error rates under high streaming conditions.