LNPE enhances local connections in embeddings using extended neighbor propagation.
problem Improving local connections and interactions in nonlinear dimensionality reduction.
method Inspired by GCN, LNPE extends 1-hop neighbors to n-hop neighbors in LLE.
result LNPE produces more faithful and robust embeddings with better topological and geometrical properties.
Indirect attacks can fool graph classifiers even with poisoned neighbors.
problem How to evaluate and defend graph convolutional neural networks against indirect adversarial attacks.
method Proposed a method to generate adversarial perturbations on a single node far from the target.
result 99% attack success rate within two-hops from the target in two datasets.
Study shows SNN graph Laplacians converge to k-NN graph Laplacians under large scale asymptotics.
problem Understanding the convergence of SNN graph Laplacians to k-NN graph Laplacians.
method Analyzing the asymptotic behavior of SNN and k-NN graph Laplacians.
result The graph Laplacians of SNN and k-NN graphs converge to the same limit under large scale asymptotics.
LAGCN improves GCN performance by identifying and using valuable neighbors.
problem Existing GCN models do not identify valuable neighbors, potentially harming performance.
method LAGCN introduces a label-aware edge classifier to refine the graph and enhance learning performance.
result LAGCN significantly improves node classification performance on benchmark datasets.
BGNN improves GNN by modeling interactions between neighbor nodes.
problem Existing GNN models fail to capture interactions between neighbor nodes, leading to suboptimal performance.
method Proposes a new graph convolution operator that augments the weighted sum with pairwise interactions of neighbor nodes.
result Empirical results show BGNN models outperform traditional GNN models in node classification accuracy.
This paper improves nearest neighbor search by learning optimal routing functions.
problem Local minima issues in greedy routing on similarity graphs.
method Learn routing function that considers global graph structure.
result Significant improvement in search performance via learning.
AdaGCN uses AdaBoost to efficiently integrate high-order neighbor knowledge in graph neural networks.
problem Efficiently exploring and exploiting knowledge from different hops of neighbors in graph neural networks.
method Incorporates AdaBoost into graph convolutional networks to integrate knowledge from high-order neighbors.
result AdaGCN achieves state-of-the-art prediction performance across different graphs and label rates.
New algorithms reduce GCN computation complexity and improve convergence.
problem Reducing the computational complexity of GCNs by controlling the number of neighbors.
method Control variate based algorithms to sample an arbitrarily small neighbor size, proving convergence to a local optimum.
result Proved algorithms converge to a local optimum of GCN with a small neighbor size.
PINE embeds graph nodes flexibly, capturing any neighbor dependency.
problem Learning flexible node representations from graph neighborhoods.
method PINE uses partial permutation invariant set functions to capture any possible neighbor dependencies.
result PINE outperforms state-of-the-art methods on various graph learning tasks.
Neighbor Mixture Model captures node correlations in graphs.
problem Modeling correlations between node labels in graphs.
method Neighbor Mixture Model (NMM) designed for efficient computation and scalability.
result NMM outperforms state-of-the-art models in various graph tasks.
A new GCN model learns higher-order neighbors without explicit adjacency matrix computation.
problem GCN's performance drops for deeper structures due to limited neighborhood information.
method Assumes higher-order neighbors are similar to first-order neighbors, learns weights through Lasso to minimize feature loss.
result HWGCN achieves state-of-the-art results on various datasets.
We study clustering algorithms based on neighborhood graphs on a random sample of data points. The question we ask is how such a graph should be constructed in order to obtain optimal clustering results. Which type of neighborhood graph should one choose, mutual k-nearest neighbor or symmetric k-nearest neighbor? What …
Method reconstructs missing wind farm data using graph theory and nearest neighbors.
problem Missing data in wind farm records due to sensor failures.
method Combines spectral graph theory and k-Nearest Neighbors to estimate missing data.
result Significant improvement in data reconstruction over existing methods.
A new graph-based clustering method for moderate-dimensional data.
problem Performance degradation of existing graph-based clustering methods in high dimensions.
method Introduces UN-CCDs using NND-based MC-SRT for covering radii determination.
result UN-CCDs provide stable and competitive performance in moderate-sized datasets.
New method improves nearest neighbor search using neural networks and graph partitioning.
problem Efficient nearest neighbor search in high-dimensional spaces.
method Developed a new framework for space partitioning using neural networks and graph partitioning.
result Neural LSH partitions outperform existing methods on standard benchmarks.
Randomized graph construction ensures giant component with fewer edges.
problem Efficiently constructing sparse graphs with good connectivity.
method Randomly connecting points to a subset of their nearest neighbors.
result A sparser graph with comparable connectivity properties.
New method constructs graphs from data efficiently, suitable for large datasets.
problem Memory and runtime limitations of traditional TMFG for large datasets.
method Uses k-Nearest Neighbors Graphs and memory management for scalable graph construction.
result Provides a parsimonious way to construct graphs for learning tasks.
New approach learns graph representations by contrasting first-order neighbors and graph diffusion views.
problem Learning node and graph level representations from graph data.
method Self-supervised approach using contrastive learning of multi-scale encodings.
result Achieves state-of-the-art performance on 8 out of 8 benchmarks.
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges …
Improves GCN by sampling neighbors and features for better node representation.
problem GCN's aggregation process treats all neighbors and features equally, leading to suboptimal node representations.
method Introduces a new convolution operation on feature maps constructed from a fixed node bandwidth, then passes to a standard GCN.
result Outperforms competing methods in semi-supervised node classification tasks.
The study bounds the effective diameter of graphs with positive Ollivier curvature.
problem Bounding the effective diameter of graphs with positive Ollivier curvature.
method Introducing reflective graphs and proving discrete Bonnet Myers theorem.
result The effective diameter bound is attained only for specific graphs.
Algorithm learns nearest neighbor graph from noisy distance queries.
problem Learning nearest neighbor graph from noisy distance samples.
method Active algorithm to find graph with high probability, analyzing query complexity.
result Empirically and theoretically efficient, needing only O(n log(n)Delta^-2) queries.
New algorithm improves similarity graph construction for nearest neighbor search.
problem Improving nearest neighbor search performance with more effective similarity graphs.
method Probabilistic model of a similarity graph learned through reinforcement learning.
result Higher recall rates achieved for the same number of distance computations.
Sharp bounds on diameter and eigenvalues for amply regular graphs.
problem Finding bounds for amply regular graphs' diameter and eigenvalues.
method New ideas relating discrete Ricci curvature to local matching properties, including a novel construction of a regular bipartite graph.
result Sharp diameter and eigenvalue bounds for amply regular graphs.
In this paper, we explore the relationship between one of the most elementary and important properties of graphs, the presence and relative frequency of triangles, and a combinatorial notion of Ricci curvature. We employ a definition of generalized Ricci curvature proposed by Ollivier in a general framework of Markov p…
LADIES improves GCN training efficiency and accuracy for large graphs.
problem Training large graph convolutional networks (GCNs) is computationally expensive.
method LADIES uses layer-dependent importance sampling to select nodes for training.
result LADIES outperforms previous methods in both time and memory efficiency.
Enhances graph neural networks by considering feature similarities in node aggregation.
problem Ignoring node feature similarities in traditional graph aggregation schemes.
method Interprets node aggregation as kernel weighting, proposing a framework that considers feature similarities.
result Proposed framework outperforms traditional GCNs in real-world applications.
The paper studies recovering hidden nearest neighbor graphs in large networks.
problem Discovering strong ties in social networks and assembling genome subsequences.
method Maximum likelihood estimator for recovering hidden 2k-nearest neighbor graphs. result The maximum likelihood estimator achieves asymptotic recovery guarantees under specific conditions.
A new method for semi-supervised classification using graph walks and reinforcement learning.
problem Efficiently classifying nodes in attributed networks with limited labeled data.
method Proposes a reinforcement learning approach to find optimal paths in the graph for classification.
result The method outperforms existing approaches on multiple datasets.
A graph clustering method that moves nodes to highest-degree neighbors.
problem Graph clustering for data with Morse regularity.
method Max-degree hill-climbing on graph nodes.
result Asymptotically consistent for random geometric graphs.
Heterophily affects GNN robustness; separating ego- and neighbor-embeddings improves defense.
problem The robustness of GNNs to adversarial attacks.
method Formalized relation between heterophily and GNN robustness; empirical analysis; design principles for improved robustness.
result Separating ego- and neighbor-embeddings increases GNN robustness.
GTEA learns node representations in temporal interaction graphs.
problem Inductive representation learning on temporal interaction graphs.
method Integrates sequence model with time encoder and self-attention scheme for edge and node embeddings.
result GTEA learns comprehensive node representations capturing temporal and structural characteristics.
Cellina uses supervised disentanglement to predict cell behavior in tissues.
problem Querying counterfactuals on tissue graphs
method Cellina framework using supervised disentanglement
result Outperforms spatially-informed and non-spatial competitors
In our previous works, we proposed a physically-inspired rule to organize the data points into an in-tree (IT) structure, in which some undesired edges are allowed to occur. By removing those undesired or redundant edges, this IT structure is divided into several separate parts, each representing one cluster. In this w…
VQ-GNN scales GNNs to large graphs using vector quantization.
problem Scaling GNNs to large graphs with stable performance and speed.
method VQ-GNN uses vector quantization to preserve all messages passed to a mini-batch of nodes, avoiding the 'neighbor explosion' problem.
result VQ-GNN achieves competitive performance on large-graph node classification and link prediction benchmarks.
DAGCN improves graph classification by learning neighbor importance and pooling.
problem Loss of early-stage information and loss of node characteristics in GCNs.
method Dual attention graph convolution and self-attention pooling.
result DAGCN outperforms state-of-the-art methods in graph classification.
Simple graphs with 12 nodes and 6 neighbors always have a 6-node subgraph.
problem Finding a specific subgraph in simple graphs.
method Proving every graph of order 12 with minimum degree 6 contains a K_6 minor.
result Simple graphs of order 12 and minimum degree 6 contain K_6 minors.
Unified framework for graph neural networks using EdgeNet.
problem Leveraging neural networks on graphs for structured data.
method Introducing EdgeNet architecture that allows different nodes to use different parameters for neighbor information.
result Unified formulation of GCNNs and GATs, highlighting their similarities and differences.
GmCN adapts GCN feature aggregation to improve graph learning.
problem Fixed neighborhood graph aggregation in GCNs is biased and can be affected by graph structure noises.
method GmCN allows nodes to adaptively select optimal neighbors for feature aggregation.
result GmCN improves graph learning effectiveness through adaptive neighbor selection.
New algorithms detect outliers in high-dimensional data with arbitrary shapes.
problem Challenges of high dimensionality and varying cluster shapes in traditional outlier detection methods.
method Cluster Catch Digraphs (CCDs) and their variants (U-MCCD, UN-MCCD, SU-MCCD, SUN-MCCD).
result U-MCCD efficiently identifies outliers with high true negative rates, and SU-MCCD improves handling of non-uniform clusters.
HAGs eliminate redundant computations in GNNs, improving training efficiency.
problem Redundant computations in GNNs leading to inefficiencies.
method Hierarchically Aggregated computation Graphs (HAGs) to manage and eliminate redundant computations.
result Significant improvement in training efficiency (up to 2.8x) with HAGs.
k Nearest Neighbors (kNN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially when a very limited amount of labeled samples are available. In this paper, we pro…
SNTG improves semi-supervised learning by considering data connections.
problem Improving semi-supervised learning performance with fewer labeled data.
method Constructs a graph from teacher model predictions and learns smooth representations of similar neighboring points.
result Achieves state-of-the-art results on semi-supervised learning benchmarks.
Improved graph attention model for noisy graphs.
problem Understanding and improving graph attention in noisy graphs.
method Proposes SuperGAT, a self-supervised graph attention network.
result SuperGAT learns more expressive attention by encoding edges.
We present a simple, yet effective, approach to Semi-Supervised Learning. Our approach is based on estimating density-based distances (DBD) using a shortest path calculation on a graph. These Graph-DBD estimates can then be used in any distance-based supervised learning method, such as Nearest Neighbor methods and SVMs…
Graph Denoising Policy Network learns robust representations from noisy graphs.
problem Noise sensitivity in graph representation learning.
method Reinforcement learning to select signal neighborhoods and aggregate features.
result Significantly outperforms state-of-the-art methods on node classification tasks.
Graph diffusion convolution improves graph learning by leveraging generalized graph diffusion.
problem Noisy and arbitrarily defined edges in real graphs.
method Graph diffusion convolution (GDC) using generalized graph diffusion like heat kernel and personalized PageRank.
result Replacing message passing with graph diffusion convolution leads to significant performance improvements.
Enhances GNNs by capturing node relationships, outperforming 2-WL test.
problem Inability of conventional GNNs to fully capture node relationships due to permutation invariance.
method Develops permutation-sensitive aggregation mechanism using permutation groups.
result Proves superior expressivity compared to 2-WL test and not less than 3-WL test.