Related papers: Topological Data Analysis of Time Series Data for …
Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…
Topological Data Analysis (TDA) has recently gained significant attention in the field of financial prediction. However, the choice of point cloud construction methods, topological feature representations, and classification models has a…
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…
Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…
Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these…
In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two…
Firm financials are well established as return predictors, being the inspiration for a large set of anomalies in the asset pricing literature. Employing topological data analysis we revisit the question of association between seven of the…
This paper uses topological data analysis (TDA) tools and introduces a data-driven clustering-based stock selection strategy tailored for sparse portfolio construction. Our asset selection strategy exploits the topological features of stock…
Topological Data Analysis (TDA) has emerged as a powerful tool for extracting meaningful features from complex data structures, driving significant advancements in fields such as neuroscience, biology, machine learning, and financial…
Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…
Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity…
We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pronounced topological…
Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…
We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence…
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…
A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topological data analysis (TDA) methods have been applied to…
Data is essential to performing time series analysis utilizing machine learning approaches, whether for classic models or today's large language models. A good time-series dataset is advantageous for the model's accuracy, robustness, and…
Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…
We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the…
Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…