Related papers: Persistent Homology for Breast Tumor Classificatio…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
Breast cancer is the most commonly diagnosed cancer in women and a leading cause of cancer death worldwide. Screening mammography reduces mortality, yet interpretation still suffers from substantial false negatives and false positives, and…
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…
The advent of digital pathology presents opportunities for computer vision for fast, accurate, and objective solutions for histopathological images and aid in knowledge discovery. This work uses deep learning to predict genomic biomarkers -…
Computer aided detection and diagnosis systems based on deep learning have shown promising performance in breast cancer detection. However, there are cases where the obtained results lack justification. In this study, our objective is to…
Accurate and interpretable brain tumor classification from medical imaging remains a challenging problem due to the high dimensionality and complex structural patterns present in magnetic resonance imaging (MRI). In this study, we propose a…
The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from…
3-D shape is important to chemistry, but how important? Machine learning works best when the inputs are simple and match the problem well. Chemistry datasets tend to be very small compared to those generally used in machine learning so we…
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,…
Accurate diagnosis of breast cancer in histopathology images is challenging due to the heterogeneity of cancer cell growth as well as of a variety of benign breast tissue proliferative lesions. In this paper, we propose a practical and…
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…
Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
Identifying molecular signatures from complex disease patients with underlying symptomatic similarities is a significant challenge in the analysis of high dimensional multi-omics data. Topological data analysis (TDA) provides a way of…
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…