Related papers: Using Topological Data Analysis to classify Encryp…

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural…

Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Clustering is one of the most common tasks of Machine Learning. In this paper we examine how ideas from topology can be used to improve clustering techniques.

A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a…

Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…

Features such as photon rings, jets, or hot. spots can leave particular topological signatures in a black hole image. As such, topological data analysis can be used to characterize images resulting from high resolution observations…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

In this paper, we develop topological data analysis methods for classification tasks on univariate time series. As an application, we perform binary and ternary classification tasks on two public datasets that consist of physiological…

Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…

We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…