Related papers: Unsupervised topological learning for identificati…

Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…

Microscopic examination of slides prepared from tissue samples is the primary tool for detecting and classifying cancerous lesions, a process that is time-consuming and requires the expertise of experienced pathologists. Recent advances in…

Unsupervised machine learning methods are used to identify structural changes using the melting point transition in classical molecular dynamics simulations as an example application of the approach. Dimensionality reduction and clustering…

One endeavour of modern physical chemistry is to use bottom-up approaches to design materials and drugs with desired properties. Here we introduce an atomistic structure learning algorithm (ASLA) that utilizes a convolutional neural network…

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)…

This paper presents a novel approach to learn and detect distinctive regions on 3D shapes. Unlike previous works, which require labeled data, our method is unsupervised. We conduct the analysis on point sets sampled from 3D shapes, then…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

Understanding the dynamical processes that govern the performance of functional materials is essential for the design of next generation materials to tackle global energy and environmental challenges. Many of these processes involve the…

The high-throughput screening of periodic inorganic solids using machine learning methods requires atomic positions to encode structural and compositional details into appropriate material descriptors. These atomic positions are not…

Topological Data Analysis (TDA) is a novel, and relatively new approach to analysing high-dimensional data sets. It does this by focussing on global properties like the shape and connectivity of the data giving it a significant advantage…

Nowadays, Machine Learning and Deep Learning methods have become the state-of-the-art approach to solve data classification tasks. In order to use those methods, it is necessary to acquire and label a considerable amount of data; however,…

Unsupervised machine learning, and in particular data clustering, is a powerful approach for the analysis of datasets and identification of characteristic features occurring throughout a dataset. It is gaining popularity across scientific…

Unsupervised clustering is one of the most fundamental challenges in machine learning. A popular hypothesis is that data are generated from a union of low-dimensional nonlinear manifolds; thus an approach to clustering is identifying and…

The Landau description of phase transitions relies on the identification of a local order parameter that indicates the onset of a symmetry-breaking phase. In contrast, topological phase transitions evade this paradigm and, as a result, are…

We show that unsupervised machine learning can be used to learn physical and chemical transformation pathways from the observational microscopic data, as demonstrated for atomically resolved images in Scanning Transmission Electron…

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…

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…

Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries also from noisy and imperfect data and…

Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…

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…