Related papers: Persistence-Augmented Neural Networks
Deep artificial neural networks require a large corpus of training data in order to effectively learn, where collection of such training data is often expensive and laborious. Data augmentation overcomes this issue by artificially inflating…
In recent years, many data augmentation techniques have been proposed to increase the diversity of input data and reduce the risk of overfitting on deep neural networks. In this work, we propose an easy-to-implement and model-free data…
Deep topological data analysis (TDA) offers a principled framework for capturing structural invariants such as connectivity and cycles that persist across scales, making it a natural fit for anomaly segmentation (AS). Unlike thresholdbased…
Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…
We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pronounced topological…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
Graph neural networks, a powerful deep learning tool to model graph-structured data, have demonstrated remarkable performance on numerous graph learning tasks. To address the data noise and data scarcity issues in deep graph learning, the…
Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological summary that can be easily combined with tools from statistics and machine learning.…
The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training process, and interpret their outputs. In this paper, we propose a novel approach to investigate…
Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable,…
Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple…
Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…
Large time-varying graphs are increasingly common in financial, social and biological settings. Feature extraction that efficiently encodes the complex structure of sparse, multi-layered, dynamic graphs presents computational and…
The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks…
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…
Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…
We propose a simple yet novel data augmentation method for general data modalities based on energy-based modeling and principles from information geometry. Unlike most existing learning-based data augmentation methods, which rely on…
Understanding how the spatial structure of blood vessel networks relates to their function in healthy and abnormal biological tissues could improve diagnosis and treatment for diseases such as cancer. New imaging techniques can generate…
Recent years have witnessed an increased interest in the application of persistent homology, a topological tool for data analysis, to machine learning problems. Persistent homology is known for its ability to numerically characterize the…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…