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Found 38 papers, 16 papers with code
A simple yet effective baseline for non-attributed graph classification
We test our baseline representation for the graph classification task on a range of graph datasets.
Ranked #22 on
Graph Classification
on MUTAG
Principal Component Analysis in Space Forms
Finding a low-dimensional Riemannian affine subspace for a set of points in a space form amounts to dimensionality reduction because, as we show, any such affine subspace is isometric to a space form of the same dimension and curvature.
Generative Coarse-Graining of Molecular Conformations
Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation.
A Note on Over-Smoothing for Graph Neural Networks
In this paper, we build upon previous results \cite{oono2019graph} to further analyze the over-smoothing effect in the general graph neural network architecture.
Learning metrics for persistence-based summaries and applications for graph classification
However often in practice, the choice of the weight function should depend on the nature of the specific type of data one considers, and it is thus highly desirable to learn a best weight function (and thus metric for persistence diagrams) from labelled data.
Ranked #1 on
Graph Classification
on NCI109
Graph Classification
Computational Geometry
Implicit Graphon Neural Representation
We also show that our model is suitable for graph representation learning and graph generation.
On the Connection Between MPNN and Graph Transformer
Graph Transformer (GT) recently has emerged as a new paradigm of graph learning algorithms, outperforming the previously popular Message Passing Neural Network (MPNN) on multiple benchmarks.
Ranked #8 on
Node Classification
on PascalVOC-SP
Graph Reconstruction by Discrete Morse Theory
Specifically, first, leveraging existing theoretical understanding of persistence-guided discrete Morse cancellation, we provide a simplified version of the existing discrete Morse-based graph reconstruction algorithm.
Computational Geometry
Neural Approximation of Graph Topological Features
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods.
Graph Coarsening with Neural Networks
As large-scale graphs become increasingly more prevalent, it poses significant computational challenges to process, extract and analyze large graph data.
DE-HNN: An effective neural model for Circuit Netlist representation
Using the input and output data of the tools from past designs, one can attempt to build a machine learning model that predicts the outcome of a design in significantly shorter time than running the tool.
Understanding Oversquashing in GNNs through the Lens of Effective Resistance
We propose to use total effective resistance as a bound of the total amount of oversquashing in a graph and provide theoretical justification for its use.
The Numerical Stability of Hyperbolic Representation Learning
Given the exponential growth of the volume of the ball w. r. t.
Distances for Markov Chains, and Their Differentiation
Recently, in the graph learning and optimization communities, a range of new approaches have been developed for comparing graphs with node attributes, leveraging ideas such as the Optimal Transport (OT) and the Weisfeiler-Lehman (WL) graph isomorphism test.
Cycle Invariant Positional Encoding for Graph Representation Learning
To efficiently encode the space of all cycles, we start with a cycle basis (i. e., a minimal set of cycles generating the cycle space) which we compute via the kernel of the 1-dimensional Hodge Laplacian of the input graph.
Unperturbed: spectral analysis beyond Davis-Kahan
Classical matrix perturbation results, such as Weyl's theorem for eigenvalues and the Davis-Kahan theorem for eigenvectors, are general purpose.
Graphons, mergeons, and so on!
In this work we develop a theory of hierarchical clustering for graphs.
Beyond Hartigan Consistency: Merge Distortion Metric for Hierarchical Clustering
In this paper we identify two limit properties, separation and minimality, which address both over-segmentation and improper nesting and together imply (but are not implied by) Hartigan consistency.
A Topological Regularizer for Classifiers via Persistent Homology
In particular, our measurement of topological complexity incorporates the importance of topological features (e. g., connected components, handles, and so on) in a meaningful manner, and provides a direct control over spurious topological structures.
Learning with Fredholm Kernels
In this paper we propose a framework for supervised and semi-supervised learning based on reformulating the learning problem as a regularized Fredholm integral equation.
Data Skeletonization via Reeb Graphs
While such data is often high-dimensional, it is of interest to approximate it with a low-dimensional or even one-dimensional space, since many important aspects of data are often intrinsically low-dimensional.
Composing Tree Graphical Models with Persistent Homology Features for Clustering Mixed-Type Data
Clustering data with both continuous and discrete attributes is a challenging task.
Road Network Reconstruction from Satellite Images with Machine Learning Supported by Topological Methods
Next, in a fully automatic framework, we leverage the power of the discrete-Morse based graph reconstruction algorithm to train a CNN from a collection of images without labelled data and use the same algorithm to produce the final output from the segmented images created by the trained CNN.
Understanding the Power of Persistence Pairing via Permutation Test
For shape segmentation and classification, however, we note that persistence pairing shows significant power on most of the benchmark datasets, and improves over both summaries based on merely critical values, and those based on permutation tests.
Detection and skeletonization of single neurons and tracer injections using topological methods
Neuroscientific data analysis has traditionally relied on linear algebra and stochastic process theory.
Topology-Aware Segmentation Using Discrete Morse Theory
In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern.
Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graph
Comparisons among predictions inferred from training the CNN and those from graph convolutional neural networks (GNN) with and without the equivariant constraint indicate that the equivariant graph neural network seems to perform better than the CNN and GNN without enforcing equivariant constraints.
NN-Baker: A Neural-network Infused Algorithmic Framework for Optimization Problems on Geometric Intersection Graphs
This leads to a mixed algorithmic-ML framework, which we call NN-Baker that has the capacity to approximately solve a family of graph optimization problems (e. g, maximum independent set and minimum vertex cover) in time linear to input graph size, and only polynomial to approximation parameter.
Convergence of Invariant Graph Networks
Building upon this result, we prove the convergence of $k$-IGN under the model of \citet{ruiz2020graphon}, where we access the edge weight but the convergence error is measured for graphon inputs.
Weisfeiler-Lehman meets Gromov-Wasserstein
The WL distance is polynomial time computable and is also compatible with the WL test in the sense that the former is positive if and only if the WL test can distinguish the two involved graphs.
On the Convergence of Optimizing Persistent-Homology-Based Losses
Topological loss based on persistent homology has shown promise in various applications.
Learning Ultrametric Trees for Optimal Transport Regression
For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the space.
The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNs
This new interpretation connects the WL distance to the literature on distances for stochastic processes, which also makes the interpretation of the distance more accessible and intuitive.
Universal Representation of Permutation-Invariant Functions on Vectors and Tensors
Restricting the domain of the functions to finite multisets of $D$-dimensional vectors, Deep Sets also provides a \emph{universal approximation} that requires a latent space dimension of $O(N^D)$ -- where $N$ is an upper bound on the size of input multisets.
NN-Steiner: A Mixed Neural-algorithmic Approach for the Rectilinear Steiner Minimum Tree Problem
On the methodology front, we propose NN-Steiner, which is a novel mixed neural-algorithmic framework for computing RSMTs that leverages the celebrated PTAS algorithmic framework of Arora to solve this problem (and other geometric optimization problems).
Position Paper: Challenges and Opportunities in Topological Deep Learning
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models.
Comparing Graph Transformers via Positional Encodings
The distinguishing power of graph transformers is closely tied to the choice of positional encoding: features used to augment the base transformer with information about the graph.
On the Theoretical Expressive Power and the Design Space of Higher-Order Graph Transformers
In this paper, we provide a systematic study of the theoretical expressive power of order-$k$ graph transformers and sparse variants.
