GMT improves interpretability of XGNNs by approximating SubMT.
problem Limited understanding of existing interpretable subgraph learning methods.
method Formulated subgraph multilinear extension (SubMT) and designed GMT architecture.
result GMT outperforms state-of-the-art in both interpretability and generalizability.
Let Γ be a finite graph and let Γe be its extension graph. We inductively define a sequence {Γi} of finite induced subgraphs of Γe through successive applications of an operation called "doubling along a star". Then we show that every finite induced subgraph of Γe is iso…
The main results of our paper deal with the lifting problem for multilinear differential operators between complexes of horizontal de Rham forms on the infinite jet bundle. We answer the question when does an n-multilinear differential operator from the space of (N,0)-forms (where N is the dimension of the base) to the…
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H. Gloeckner and K.-H. Neeb), without any restriction on the dimension or on the cha…
Derives a primal-dual MLSVD formulation for multilinear data.
problem Efficiently decompose multilinear data for signal analysis and deep learning.
method Kernelizable primal-dual formulation of MLSVD.
result Derives a new MLSVD formulation with computational advantages.
Proposes MLDP for modeling multilinear data.
problem Handling data with interactions from multiple factors.
method Combines Dirichlet processes with multilinear factor analysis.
result Achieved state-of-the-art performance on real-world data.
New method forecasts multilinear data using tensor autoregression.
problem Forecasting 2D data in big data.
method L-Transform Tensor autoregressive (L-TAR) method.
result Statistical independence achieved through invertible discrete linear transforms.
Proposes GIB for recognizing informative subgraphs in graphs.
problem Recognizing a subgraph that is maximally informative yet compressive.
method Graph Information Bottleneck (GIB) framework, mutual information estimator, bi-level optimization, connectivity loss.
result IB-subgraph improves graph classification, interpretation, and denoising.
Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means that for higher order data like matrices or more generally tensors, data should be…
Geometrically, tensors of fixed rank form a minimal submanifold.
problem Understanding the geometric properties of tensors of fixed rank.
method Geometric analysis of tensors in Euclidean space.
result Real tensors of fixed multilinear rank form a minimal submanifold.
Mining discriminative features for graph data has attracted much attention in recent years due to its important role in constructing graph classifiers, generating graph indices, etc. Most measurement of interestingness of discriminative subgraph features are defined on certain graphs, where the structure of graph objec…
Unified multilinear model for causal factor disentanglement.
problem Disentangling causal factors from complex data without direct manipulation.
method Hierarchical block multilinear factorization (M-mode Block SVD) and incremental approach.
result Interpretable object representation robust to occlusion and reduced training data.
Four algorithms improve sparse tensor BR1Approx with theoretical guarantees.
problem Sparse tensor best rank-1 approximation.
method Four approximation algorithms exploiting multilinearity and sparsity.
result Theoretical worst-case approximation lower bounds for all algorithms.
Neural network for subgraph similarity computation with pruning.
problem Computing subgraph similarity between a target and query graph.
method Convert pruning to node relabeling, relax to differentiable problem, design neural network for SED computation.
result Establishes new state-of-the-art results across multiple benchmark datasets.
TopInG improves graph interpretability using persistent homology.
problem Lack of interpretability in Graph Neural Networks (GNNs).
method TopInG uses persistent homology to identify persistent rationale subgraphs in graphs.
result TopInG improves predictive accuracy and interpretability compared to state-of-the-art methods.
StrGNN detects anomalies in dynamic graphs by analyzing subgraphs and temporal features.
problem Detecting anomalies in dynamic graphs with structural changes.
method StrGNN is an end-to-end model that uses structural subgraphs and temporal features for anomaly detection.
result StrGNN effectively detects anomalies in dynamic graphs, as shown by extensive experiments.
RAW-Explainer generates interpretable subgraph explanations for link predictions in knowledge graphs.
problem Interpreting GNN predictions for link prediction in heterogeneous settings is challenging.
method RAW-Explainer uses random walk objective and neural network to generate connected, concise subgraph explanations.
result RAW-Explainer strikes a balance between explanation quality and computational efficiency.
Ripple Walk Training tackles graph neural network training issues for large and deep graphs.
problem Neighbors explosion, node dependence, and oversmoothing in large and deep GNNs.
method Subgraph-based training framework with Ripple Walk Sampler for high-quality subgraph sampling.
result RWT improves training efficiency and reduces space complexity for deep and large GNNs.
New algorithm solves ℓ0-norm constrained multilinear logistic regression for tensor data.
problem Non-convex and nonsmooth ℓ0-norm constraints in multilinear logistic regression. method APALM+ method for globally convergent optimization. result APALM+ ensures convergence to a first-order critical point. Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging problem is related to determination of model complexity (i.e., multilinear rank), e…
Branch-and-bound (BnB) algorithms are widely used to solve combinatorial problems, and the performance crucially depends on its branching heuristic.In this work, we consider a typical problem of maximum common subgraph (MCS), and propose a branching heuristic inspired from reinforcement learning with a goal of reaching…
In this paper we present a new model and an algorithm for unsupervised clustering of 2-D data such as images. We assume that the data comes from a union of multilinear subspaces (UOMS) model, which is a specific structured case of the much studied union of subspaces (UOS) model. For segmentation under this model, we de…
Wide neural networks become linear, but adding bottlenecks makes them bilinear or multilinear.
problem Understanding the transition of neural networks from linearity to higher-order functions.
method Analyzing the behavior of randomly initialized wide neural networks with and without bottleneck layers.
result Bottleneck layers transform the network's function from linear to bilinear or multilinear.
We present graph partition neural networks (GPNN), an extension of graph neural networks (GNNs) able to handle extremely large graphs. GPNNs alternate between locally propagating information between nodes in small subgraphs and globally propagating information between the subgraphs. To efficiently partition graphs, we …
VISTA learns causal structures by integrating local subgraphs, improving accuracy and efficiency.
problem Efficiently learning causal structures from high-dimensional observational data.
method VISTA decomposes the global causal structure learning problem into local subgraphs based on Markov Blankets, integrating them via a weighted voting mechanism.
result VISTA achieves notable improvements in accuracy and efficiency over existing methods.
Extends RRR to capture nonlinear interactions in multi-response regression.
problem Complex relationships in real-world data cannot be adequately modeled by linear interactions.
method Introduces Higher Order Reduced Rank Regression (HORRR) using tensor representations and Tucker decomposition.
result HORRR can capture nonlinear interactions in multi-response regression.
Study uses random matrix theory to improve tensor approximation accuracy.
problem Improving tensor approximation accuracy in the presence of noise.
method Random matrix theory applied to tensor unfoldings.
result Characterizes spectral behavior of tensor unfoldings and predicts reconstruction performance.
SubGNN tackles subgraph prediction challenges in graphs.
problem Subgraphs in graphs are challenging to predict due to their internal topology and external connectivity.
method SubGNN introduces a novel subgraph routing mechanism to learn disentangled subgraph representations.
result SubGNN achieves considerable performance gains on subgraph classification tasks, outperforming strong baseline methods.
Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor projection or tensor-to-vector projection (TVP). However, under the TVP setting, i…
Structure learning of Bayesian networks has always been a challenging problem. Nowadays, massive-size networks with thousands or more of nodes but fewer samples frequently appear in many areas. We develop a divide-and-conquer framework, called partition-estimation-fusion (PEF), for structure learning of such big networ…
Proposes FMPCA for federated tensor data dimensionality reduction.
problem Integration of MPCA into federated learning.
method Federated Multilinear Principal Component Analysis (FMPCA).
result FMPCA preserves performance of traditional MPCA in federated learning.
The paper introduces subgraph nomination for finding similar subgraphs in networks.
problem Finding similar subgraphs in networks using example subgraphs.
method Formalizes subgraph nomination framework with user-supervised retrieval.
result User-supervised retrieval improves performance in subgraph nomination.
Neumann eigenmaps improve landmark-based diffusion map embeddings.
problem Landmark-based diffusion map embeddings can be computationally inefficient and unstable.
method NeuMaps use a renormalized Neumann Laplacian for eigendecomposition, incorporating landmarks as a subgraph.
result NeuMaps offer a computationally efficient and stable embedding method.
NeuroMatch efficiently matches subgraphs in large graphs using neural networks.
problem Determining the presence and location of a query graph in a large target graph.
method NeuroMatch decomposes graphs into subgraphs, embeds them using graph neural networks, and matches them directly in the embedding space.
result NeuroMatch is 100x faster and 18% more accurate than existing methods.
New sampling method estimates Shapley values more accurately.
problem Exponential time complexity of computing Shapley values.
method Multilinear sampling algorithm based on game theory.
result Our method reduces variance and provides more accurate Shapley value estimations.
In practical machine learning systems, graph based data representation has been widely used in various learning paradigms, ranging from unsupervised clustering to supervised classification. Besides those applications with natural graph or network structure data, such as social network analysis and relational learning, …
Unified framework for subgraph-enhanced GNNs, improving prediction accuracy and reducing computation time.
problem Limited understanding of subgraph-enhanced GNNs and their relation to the Weisfeiler-Leman hierarchy.
method Theoretical framework, theoretical expressivity results, and data-driven subgraph sampling methods.
result Data-driven subgraph-enhanced GNNs outperform non-data-driven methods in predictive performance.
Study area-minimizing subgraphs in integer lattices.
problem Finding the most efficient subgraphs in integer lattices.
method Formulated functions of bounded variations, classified subgraphs in 2D, proved properties in higher dimensions.
result Classified area-minimizing subgraphs in 2D integer lattice up to isomorphisms.
We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by …
Given a multifunction from X to the k−fold symmetric product Symk(X), we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixe…
GNNS uses graph neural networks to efficiently estimate subgraph frequency distributions.
problem Efficiently calculating subgraph frequency distributions in large networks.
method Graph Neural Networks (GNNS) for sampling and estimating subgraph frequencies.
result GNNS achieves comparable accuracy with a significant speedup of three orders of magnitude.
New model generates unseen attribute combinations from limited data.
problem Lack of generalization in deep generative models for unseen attribute combinations.
method Introduces multilinear latent conditioning to capture multiplicative interactions.
result Demonstrates effectiveness on MNIST, Fashion-MNIST, and CelebA datasets.
SubSearch detects graph outliers and estimates SBM parameters robustly.
problem Real-world graphs often deviate from ideal SBM assumptions.
method Subgraph search to find subgraphs that align with SBM assumptions.
result SubSearch accurately estimates SBM parameters and detects outliers.
We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We conduct an extensive study of intrinsic scale for several networks, ranging fro…
We consider the densest k-subgraph problem, which seeks to identify the k-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We propose a new convex relaxation for the densest k-subgraph problem, based on a nucle…
RevTrack identifies suspicious subgraphs on blockchain for AML.
problem Detecting money laundering in cryptocurrency transactions.
method Graph-based machine learning, tracking initial senders and final receivers.
result RevClassify outperforms state-of-the-art subgraph classification techniques in cost and accuracy.
Faster algorithm for generalized mean densest subgraph problem.
problem Finding subgraphs with highest average p-th-power degree. method GENPEEL++ algorithm, which yields (2(p+1))1/p-approximation for p∈[1,+∞) with time complexity O(m(logn)). result GENPEEL++ algorithm provides faster and more efficient solution for generalized mean densest subgraph problem.