Related papers: On topological data analysis for structural dynami…
Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…
This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex…
Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…
Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…
In the context of rapid urbanization, understanding the patterns of urban residents' activities and mobility is crucial for optimizing transportation systems and enhancing urban management efficiency. This study addresses the limitations of…
Permutation Entropy (PE) is a powerful tool for quantifying the complexity of a signal which includes measuring the regularity of a time series. Additionally, outside of entropy and information theory, permutations have recently been…
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…
We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN). We compute the persistent homology of the activation data for each layer of the network and summarize…
Interleaving distances are used widely in Topological Data Analysis (TDA) as a tool for comparing topological signatures of datasets. The theory of interleaving distances has been extended through various category-theoretic constructions,…
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…
We present a novel method for analyzing geospatial trajectory data using topological data analysis (TDA) to identify a specific class of anomalies, commonly referred to as crop circles, in AIS data. This approach is the first of its kind to…
Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data. The use of machine learning algorithms on the space of persistence diagrams proves to…
This application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence…
Topological data analysis (TDA) has emerged as an effective approach in data science, with its key technique, persistent homology, rooted in algebraic topology. Although alternative approaches based on differential topology, geometric…
Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known…
In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…