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Found 61 papers, 36 papers with code
Principal Curvatures Estimation with Applications to Single Cell Data
The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets.
No Metric to Rule Them All: Toward Principled Evaluations of Graph-Learning Datasets
Observing that graph-learning datasets uniquely combine two modes -- the graph structure and the node features -- , we introduce RINGS, a flexible and extensible mode-perturbation framework to assess the quality of graph-learning datasets based on dataset ablations -- i. e., by quantifying differences between the original dataset and its perturbed representations.
Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform
This overview article makes the case for how topological concepts can enrich research in machine learning.
Graph Classification Gaussian Processes via Hodgelet Spectral Features
The problem of classifying graphs is ubiquitous in machine learning.
Generative Topology for Shape Synthesis
The Euler Characteristic Transform (ECT) is a powerful invariant for assessing geometrical and topological characteristics of a large variety of objects, including graphs and embedded simplicial complexes.
Detecting and Approximating Redundant Computational Blocks in Neural Networks
In this paper, we investigate the emergence of these internal similarities across different layers in diverse neural architectures, showing that similarity patterns emerge independently of the datataset used.
MANTRA: The Manifold Triangulations Assemblage
The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting higher-order structures in the data, especially in topological deep learning (TDL), which designs neural networks on higher-order domains such as simplicial complexes.
Diss-l-ECT: Dissecting Graph Data with local Euler Characteristic Transforms
The Euler Characteristic Transform (ECT) is an efficiently-computable geometrical-topological invariant that characterizes the global shape of data.
CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphs
In this work, we introduce a novel method that extracts information about higher-order structures in the graph while still using the efficient low-dimensional persistent homology algorithm.
Characterizing Physician Referral Networks with Ricci Curvature
Identifying (a) systemic barriers to quality healthcare access and (b) key indicators of care efficacy in the United States remains a significant challenge.
Persistent Homology via Ellipsoids
This complex is based on the idea that ellipsoids aligned with tangent directions better approximate the data compared to conventional (Euclidean) balls centered at sample points that are used in the construction of Rips and Alpha complexes, for instance.
The Manifold Density Function: An Intrinsic Method for the Validation of Manifold Learning
We introduce the manifold density function, which is an intrinsic method to validate manifold learning techniques.
Position: Topological Deep Learning is the New Frontier for Relational Learning
At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.
Mapping the Multiverse of Latent Representations
Echoing recent calls to counter reliability and robustness concerns in machine learning via multiverse analysis, we present PRESTO, a principled framework for mapping the multiverse of machine-learning models that rely on latent representations.
Simplicial Representation Learning with Neural $k$-Forms
In this paper, we take a different approach, focusing on leveraging geometric information from simplicial complexes embedded in $\mathbb{R}^n$ using node coordinates.
Metric Space Magnitude for Evaluating the Diversity of Latent Representations
We develop a family of magnitude-based measures of the intrinsic diversity of latent representations, formalising a novel notion of dissimilarity between magnitude functions of finite metric spaces.
Differentiable Euler Characteristic Transforms for Shape Classification
The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs.
Filtration Surfaces for Dynamic Graph Classification
Existing approaches for classifying dynamic graphs either lift graph kernels to the temporal domain, or use graph neural networks (GNNs).
Topologically Regularized Multiple Instance Learning to Harness Data Scarcity
In biomedical data analysis, Multiple Instance Learning (MIL) models have emerged as a powerful tool to classify patients' microscopy samples.
Evaluating the "Learning on Graphs" Conference Experience
With machine learning conferences growing ever larger, and reviewing processes becoming increasingly elaborate, more data-driven insights into their workings are required.
MAGNet: Motif-Agnostic Generation of Molecules from Shapes
Recent advances in machine learning for molecules exhibit great potential for facilitating drug discovery from in silico predictions.
Metric Space Magnitude and Generalisation in Neural Networks
Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive.
Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices
We also show a favourable property, namely injectivity and discuss the stability of the topological loss function based on the Euler Characteristic Transform.
On the Expressivity of Persistent Homology in Graph Learning
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification.
Curvature Filtrations for Graph Generative Model Evaluation
Graph generative model evaluation necessitates understanding differences between graphs on the distributional level.
Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework
Bridging geometry and topology, curvature is a powerful and expressive invariant.
Topological Singularity Detection at Multiple Scales
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research.
A Diffusion Model Predicts 3D Shapes from 2D Microscopy Images
Diffusion models are a special type of generative model, capable of synthesising new data from a learnt distribution.
On the Surprising Behaviour of node2vec
Graph embedding techniques are a staple of modern graph learning research.
All the World's a (Hyper)Graph: A Data Drama
We introduce Hyperbard, a dataset of diverse relational data representations derived from Shakespeare's plays.
Taxonomy of Benchmarks in Graph Representation Learning
Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry.
Diffusion Curvature for Estimating Local Curvature in High Dimensional Data
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature.
Time-inhomogeneous diffusion geometry and topology
From a geometric perspective, we obtain convergence bounds based on the smallest transition probability and the radius of the data, whereas from a spectral perspective, our bounds are based on the eigenspectrum of the diffusion kernel.
Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction
We propose to complement geometrical shape information by including multi-scale topological features, such as connected components, cycles, and voids, in the reconstruction loss.
On Measuring Excess Capacity in Neural Networks
We study the excess capacity of deep networks in the context of supervised classification.
Weisfeiler and Leman go Machine Learning: The Story so far
In recent years, algorithms and neural architectures based on the Weisfeiler--Leman algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a powerful tool for machine learning with graphs and relational data.
Interpretability Aware Model Training to Improve Robustness against Out-of-Distribution Magnetic Resonance Images in Alzheimer's Disease Classification
Owing to its pristine soft-tissue contrast and high resolution, structural magnetic resonance imaging (MRI) is widely applied in neurology, making it a valuable data source for image-based machine learning (ML) and deep learning applications.
The magnitude vector of images
Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric.
Towards a Taxonomy of Graph Learning Datasets
Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data.
Predicting sepsis in multi-site, multi-national intensive care cohorts using deep learning
Here, we developed and validated a machine learning (ML) system for the prediction of sepsis in the ICU.
Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions
Graph generative models are a highly active branch of machine learning.
Exploring epithelial-cell calcium signaling with geometric and topological data analysis
However the function of calcium signaling in epithelial cells is not well understood.
Topological Graph Neural Networks
Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles.
Exploring the Geometry and Topology of Neural Network Loss Landscapes
This suggests that qualitative and quantitative examination of the loss landscape geometry could yield insights about neural network generalization performance during training.
Topological Data Analysis of copy number alterations in cancer
Identifying subgroups and properties of cancer biopsy samples is a crucial step towards obtaining precise diagnoses and being able to perform personalized treatment of cancer patients.
Image analysis for Alzheimer's disease prediction: Embracing pathological hallmarks for model architecture design
Alzheimer's disease (AD) is associated with local (e. g. brain tissue atrophy) and global brain changes (loss of cerebral connectivity), which can be detected by high-resolution structural magnetic resonance imaging.
Graph Kernels: State-of-the-Art and Future Challenges
Graph-structured data are an integral part of many application domains, including chemoinformatics, computational biology, neuroimaging, and social network analysis.
Challenging Euclidean Topological Autoencoders
Topological autoencoders (TopoAE) have demonstrated their capabilities for performing dimensionality reduction while at the same time preserving topological information of the input space.
Accelerating COVID-19 Differential Diagnosis with Explainable Ultrasound Image Analysis
Controlling the COVID-19 pandemic largely hinges upon the existence of fast, safe, and highly-available diagnostic tools.
Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence
We observe significant differences in both brain state trajectories and overall topological activity between adults and children watching the same movie.
Path Imputation Strategies for Signature Models of Irregular Time Series
The signature transform is a 'universal nonlinearity' on the space of continuous vector-valued paths, and has received attention for use in machine learning on time series.
Set Functions for Time Series
Despite the eminent successes of deep neural networks, many architectures are often hard to transfer to irregularly-sampled and asynchronous time series that commonly occur in real-world datasets, especially in healthcare applications.
Persistent Intersection Homology for the Analysis of Discrete Data
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets.
Topological Machine Learning with Persistence Indicator Functions
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis.
A Persistent Weisfeiler–Lehman Procedure for Graph Classification
The Weisfeiler–Lehman graph kernel exhibits competitive performance in many graph classification tasks.
Ranked #1 on
Graph Classification
on MUTAG
(Mean Accuracy metric)
Wasserstein Weisfeiler-Lehman Graph Kernels
Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures.
Ranked #8 on
Graph Classification
on NCI1
Topological Autoencoders
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders.
Ranked #4 on
Data Augmentation
on GA1457
Graph Filtration Learning
We propose an approach to learning with graph-structured data in the problem domain of graph classification.
Machine learning for early prediction of circulatory failure in the intensive care unit
Intensive care clinicians are presented with large quantities of patient information and measurements from a multitude of monitoring systems.
Early Recognition of Sepsis with Gaussian Process Temporal Convolutional Networks and Dynamic Time Warping
This empirical study proposes two novel approaches for the early detection of sepsis: a deep learning model and a lazy learner based on time series distances.
Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data.
