A novel method integrates feature and topology views for unsupervised graph representation learning.
problem Lack of mutual information across feature and topology views in graph representation learning.
method Proposes a multi-view representation learning module and a common representation learning module using mutual information maximization and reconstruction loss minimization.
result Demonstrates effectiveness in integrating feature and topology views, achieving comparable or better performance than supervised methods.
The main approaches for node classification in graphs are information propagation and the association of the class of the node with external information. State of the art methods merge these approaches through Graph Convolutional Networks. We here use the association of topological features of the nodes with their clas…
Topology-enhanced loss improves 3D object reconstruction from 2D images.
problem Challenges in reconstructing 3D objects from 2D images, especially capturing shape information.
method Integrates multi-scale topological features into the reconstruction loss using cubical complexes and optimal transport distance.
result Topology-aware loss substantially improves 3D reconstruction quality.
TopoFisher learns topological summaries by maximizing Fisher information, improving parameter efficiency and inference quality.
problem Simulation-based inference misses key information in low-order statistics, especially for non-Gaussian fields.
method TopoFisher uses a differentiable persistent-homology pipeline that learns topological summaries by maximizing local Gaussian Fisher information.
result TopoFisher recovers much of the available information and outperforms fixed topological vectorizations in weak gravitational lensing.
Detects graph topology changes from noisy signals using prior spectral information.
problem Detecting changes in graph topology from graph signals.
method Leverages graph filtering and subspace detection to distill problem into a CUSUM-based algorithm.
result Demonstrates the effectiveness of incorporating prior spectral signatures for change-point detection.
Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of existing Bayesian optimization algorithms can only handle vector data and canno…
Graph neural controlled differential equations learn graph dynamics from vertex observations.
problem Predicting future states of dynamical systems on graphs with limited vertex data.
method Incorporates graph topology information into NCDE to predict graph dynamics.
result Informed NCDE requires fewer parameters and lower MAE compared to previous methods.
Research predicts XRP price anomalies using graph topologies.
problem Forecasting extreme price movements in XRP cryptoasset.
method Analyzed topological features of XRP transaction graphs.
result Topological features indicate extreme price surges.
Topology-based information retrieval improves query accuracy.
problem Query accuracy in databases with complex structures.
method Dilation-invariant comparative measures of persistent homology.
result Topology-based retrieval outperforms standard methods.
Method introduces topological regularization using information filtering networks.
problem Sparse probabilistic modeling and multicollinear regression.
method Topological regularization via information filtering network.
result Direct application to L0-norm regularized problems. Enhances graph neural networks with spectral and topological information.
problem Improving graph neural networks' expressivity beyond Weisfeiler-Leman hierarchy.
method Integrates spectral information into Persistent Homology diagrams.
result SpectRe is strictly more expressive than PH and spectral information alone.
Novel TRI-GNN framework improves graph classification robustness.
problem Graph neural networks suffer from over-smoothing and vulnerability to graph perturbations.
method Integrates higher-order graph information via persistent homology and local graph structure learning.
result TRI-GNN outperforms state-of-the-art baselines on node classification tasks.
This work analyzes PPR-based node embeddings and their topological information.
problem Understanding and interpreting PPR-based node embeddings.
method Unified framework and two methods for topology recovery.
result PPR-based embeddings maintain more topological information than random walk-based embeddings.
Paper proposes learnable topological features for efficient phylogenetic inference.
problem Finding appropriate topological structures for phylogenetic inference tasks requires significant design effort and domain expertise.
method Combines raw node features with graph neural networks to automatically adapt to different tasks.
result Demonstrates effectiveness and efficiency on simulated and real data phylogenetic inference tasks.
A fundamental problem in computer vision is boundary estimation, where the goal is to delineate the boundary of objects in an image. In this paper, we propose a method which jointly incorporates geometric and topological information within an image to simultaneously estimate boundaries for objects within images with mo…
Entropy data replaces classical charts for smooth manifolds.
problem Establishing smooth structures on topological manifolds.
method Using entropy data to define admissible coordinate functions and reconstruct smooth atlases.
result Entropy-smooth structures are equivalent to classical smooth structures and stable under perturbations.
New method reduces spatial graphs while preserving their topological features.
problem Finding a smaller spatial graph with the same structure.
method Topological spatial graph coarsening approach based on triangle-aware graph filtration.
result Significant reduction in graph size while preserving topological information.
In the aftermath of the financial crisis, the growing literature on financial networks has widely documented the predictive power of topological characteristics (e.g. degree centrality measures) to explain the systemic impact or systemic vulnerability of financial institutions. In this work, we show that considering al…
Z-GCNETs uses topological data to improve time series forecasting.
problem Improving time series forecasting accuracy.
method Integrates topological data into graph convolutional networks (GCNs) using zigzag persistence.
result Z-GCNETs outperforms 13 state-of-the-art methods in traffic forecasting and Ethereum price prediction.
Graph neural networks improve topology control of power grids.
problem Grid congestion due to renewable energy and electrification.
method Investigated the effect of graph representation on GNN effectiveness for topology control.
result Heterogeneous graph representation outperforms homogeneous in topology control tasks.
Proposes GNAN model for detecting various network structures.
problem Detecting traditional communities in networks.
method GNAN model combining topology and node-attribute information.
result GNAN detects a broader range of network structures.
New TDA approach using Finsler metrics.
problem Traditional TDA concepts and methods.
method Introducing Finsler metrics for TDA.
result Relevance of Finsler metrics to TDA.
In colored graphs, node classes are often associated with either their neighbors class or with information not incorporated in the graph associated with each node. We here propose that node classes are also associated with topological features of the nodes. We use this association to improve Graph machine learning in g…
A method for vectorizing persistence diagrams simplifies topological data analysis.
problem Challenges in integrating persistence diagrams into machine learning pipelines.
method Quantized Persistence and Integral transforms of Diagrams (Qupid) using binning and discrete transforms.
result Qupid preserves highly competitive performances compared to state-of-the-art methods across various classification tasks.
New method uses iterated integrals to bridge geometric and homotopy information.
problem Lack of effective methods to connect geometric and homotopy information.
method Introducing Chen's iterated integrals on loop spaces.
result Upper bounds for Gromov's distortion and non-existence of small-volume cycles.
In this paper, we exploit minimal sensing information gathered from biologically inspired sensor networks to perform exploration and mapping in an unknown environment. A probabilistic motion model of mobile sensing nodes, inspired by motion characteristics of cockroaches, is utilized to extract weak encounter informati…
NeuroFabric proposes a method to optimize sparse network training topologies.
problem Long training times in deep neural networks due to high memory and compute requirements.
method Developed a new sparse neural network initialization scheme and evaluated various topologies.
result Identified a single optimal topology that maximizes accuracy across different datasets.
EuLearn creates diverse 3D topological datasets for machine learning.
problem Training machine learning systems to discern topological features.
method Developed novel sampling and neural network architectures for graph and manifold data.
result Incorporating topological information improves deep learning performance on EuLearn datasets.
Paper explores applying TDA to text classification, improving model performance.
problem Applying TDA to text classification is challenging due to the complexity of text geometry.
method Used word embeddings and TF-IDF vectors to extract topological features from text.
result Topological features improve classification results, especially in ensemble models.
We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective ho…
Novel tRSA combines geometry and topology for brain and model analysis.
problem Traditional RSA overlooks topological information in neural representations.
method Topological RSA (tRSA) using nonlinear monotonic transforms.
result Robust model comparisons and novel insights into neural computation.
Topological attention improves forecasting of univariate time series.
problem Forecasting univariate time series using local topological features.
method Topological attention mechanism that integrates local topological properties into forecasting models.
result Topological attention leads to state-of-the-art performance on the M4 benchmark.
The topological information is essential for studying the relationship between nodes in a network. Recently, Network Representation Learning (NRL), which projects a network into a low-dimensional vector space, has been shown their advantages in analyzing large-scale networks. However, most existing NRL methods are desi…
New method detects essential tori in mixed singularity links.
problem Detecting essential tori in mixed singularity link complements.
method Analyzing properties of defining mixed polynomials.
result Explicit criteria for essential tori existence.
Proposes a graph pooling method leveraging node proximity for hierarchical graph representation learning.
problem Efficiently exploiting the geometry of graph data for hierarchical representation learning.
method Combines node proximity with kernel representation of topology and node features for adaptive node signal similarities evaluation.
result Achieves state-of-the-art performance on graph classification benchmark datasets.
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theo…
This chapter covers methods for identifying and inferring graph topologies.
problem Identifying and inferring graph topologies from multidimensional relational data.
method Overview of methods including correlation metrics, covariance selection, kernels, structural equations, and vector autoregressions.
result Supports both batch and online learning with convergence guarantees and leverages high-order statistical information.
Correlation Networks (CNs) inherently suffer from redundant information in their network topology. Bayesian Networks (BNs), on the other hand, include only non-redundant information (from a probabilistic perspective) resulting in a sparse topology from which generalizable physical features can be extracted. We advocate…
We construct an elementary, combinatorial kind of topological quantum field theory, based on curves, surfaces, and orientations. The construction derives from contact invariants in sutured Floer homology and is essentially an elaboration of a TQFT defined by Honda--Kazez--Matic. This topological field theory stores inf…
We introduce the first unified theory for target tracking using Multiple Hypothesis Tracking, Topological Data Analysis, and machine learning. Our string of innovations are 1) robust topological features are used to encode behavioral information, 2) statistical models are fitted to distributions over these topological …
This work characterizes topological descriptors of graph products and their expressive power.
problem Capturing multiscale structural information in graph products using topological descriptors.
method Analysis of various filtrations on graph products, including Euler characteristic and persistent homology.
result Persistent homology of graph products contains more information than individual graphs.
Combines geometry and topology for analyzing hierarchical datasets.
problem Analyzing complex, hierarchical datasets with irregular structures.
method Combines manifold learning and topological data analysis.
result Superior classification results compared to state-of-the-art methods.
FCM clustering adapts to persistence diagrams for topological data analysis.
problem Integrating topological data into machine learning workflows.
method Adapting Fuzzy c-Means to persistence diagrams.
result FCM clustering captures topological structure without additional processing.
The abstract explains counterexamples in 4-manifold topology.
problem Understanding the equivalence relations on 4-manifolds.
method Explains and provides counterexamples for various equivalence relations.
result Illustrates the failure of potential implications between equivalence relations.
We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on …
We briefly review selected contributions to immersion-theoretic topology, from S. Smale's immersion theory for spheres to M. Gromov's convex integration theory, during the early "golden" period from about 1959-1973. Historical remarks are included and technical concepts are presented informally.
PHLP uses persistent homology to interpret graph link prediction.
problem Interpreting why graph neural network models perform well in link prediction.
method Employing persistent homology to analyze graph topology and extract features.
result PHLP outperforms state-of-the-art models on most benchmark datasets.
New method extracts hidden phases in binary mixtures using tubular tilings.
problem Hidden phases in binary mixtures are difficult to observe.
method Introduce tubular tilings for discretizing binary mixtures on smooth manifolds.
result Recover topological information about hidden phases from observable phases and interfaces.