Related papers: Topological Machine Learning for Mixed Numeric and…

Topology can extract the structural information in a dataset efficiently. In this paper, we attempt to incorporate topological information into a multiple output Gaussian process model for transfer learning purposes. To achieve this goal,…

Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…

Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…

Classification and prediction of heart disease is a significant problem to realize medical treatment and life protection. In this paper, persistent homology is involved to analyze electrocardiograms and a novel heart disease classification…

We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence…

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…

Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…

Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…

We establish a new theory which gives a unified topological approach to data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and…

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…

Data clustering with uneven distribution in high level noise is challenging. Currently, HDBSCAN is considered as the SOTA algorithm for this problem. In this paper, we propose a novel clustering algorithm based on what we call graph of…

Improving the precision of heart diseases detection has been investigated by many researchers in the literature. Such improvement induced by the overwhelming health care expenditures and erroneous diagnosis. As a result, various…

Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a…

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…

More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…

Topological clustering, and its main algorithm ToMATo, is a clustering method from Topological Data Analysis (TDA) which has been applied successfully in several applications during the last few years. This is due to its high versatility,…

We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…