Related papers: An Application of Topological Data Analysis to Hoc…
In medical image analysis, feature engineering plays an important role in the design and performance of machine learning models. Persistent homology (PH), from the field of topological data analysis (TDA), demonstrates robustness and…
This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a…
In machine learning, ensembles are important tools for improving the model performance. In natural language processing specifically, ensembles boost the performance of a method due to multiple large models available in open source. However,…
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine…
Topological data analysis (TDA), as a relatively recent approach, has demonstrated great potential in capturing the intrinsic and robust structural features of complex data. While persistent homology, as a core tool of TDA, focuses on…
Recently, deep learning (DL) approaches to vulnerability detection have gained significant traction. These methods demonstrate promising results, often surpassing traditional static code analysis tools in effectiveness. In this study, we…
We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances…
Cooperation is a fundamental social mechanism, whose effects on human performance have been investigated in several environments. Online games are modern-days natural settings in which cooperation strongly affects human behavior. Every day,…
For professional basketball, finding valuable and suitable players is the key to building a winning team. To deal with such challenges, basketball managers, scouts and coaches are increasingly turning to analytics. Objective evaluation of…
Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…
Single-parameter persistent homology, a key tool in topological data analysis, has been widely applied to data problems along with statistical techniques that quantify the significance of the results. In contrast, statistical techniques for…
Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited. In this work, a system developed for a leading provider of cloud…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
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…
Multi-object tracking in sports scenarios has become one of the focal points in computer vision, experiencing significant advancements through the integration of deep learning techniques. Despite these breakthroughs, challenges remain, such…
Persistent homology is a tool from Topological Data Analysis (TDA) used to summarize the topology underlying data. It can be conveniently represented through persistence diagrams. Observing a noisy signal, common strategies to infer its…
We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information…
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…
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…
Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…