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Found 50 papers, 28 papers with code
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.
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.
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.
Graph Filtration Learning
We propose an approach to learning with graph-structured data in the problem domain of graph classification.
Topological Autoencoders
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders.
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 #7 on
Graph Classification
on NCI1
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)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 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 epithelial-cell calcium signaling with geometric and topological data analysis
However the function of calcium signaling in epithelial cells is not well understood.
Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions
Graph generative models are a highly active branch of machine learning.
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.
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.
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.
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.
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.
On Measuring Excess Capacity in Neural Networks
We study the excess capacity of deep networks in the context of supervised classification.
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.
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.
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.
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.
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.
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.
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.
Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework
Bridging geometry and topology, curvature is a powerful and expressive invariant.
Curvature Filtrations for Graph Generative Model Evaluation
Graph generative model evaluation necessitates understanding differences between graphs on the distributional level.
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.
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.
Metric Space Magnitude and Generalisation in Neural Networks
Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive.
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.
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.
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.
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).
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.
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.
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.
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.
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 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.
