Related papers: ballmapper: Applying Topological Data Analysis Bal…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
Motivation: The Mapper algorithm is an essential tool to explore shape of data in topology data analysis. With a dataset as an input, the Mapper algorithm outputs a graph representing the topological features of the whole dataset. This…
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to…
The Mapper algorithm is an essential tool for visualizing complex, high dimensional data in topology data analysis (TDA) and has been widely used in biomedical research. It outputs a combinatorial graph whose structure implies the shape of…
Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However,…
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…
Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…
This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…
The mapper algorithm is a popular tool from topological data analysis for extracting topological summaries of high-dimensional datasets. In this paper, we present Mapper Interactive, a web-based framework for the interactive analysis and…
Diffusion models currently demonstrate impressive performance over various generative tasks. Recent work on image diffusion highlights the strong capabilities of Mamba (state space models) due to its efficient handling of long-range…
An understanding of the economic landscape in a world of ever increasing data necessitates representations of data that can inform policy, deepen understanding and guide future research. Topological Data Analysis offers a set of tools which…
High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…
Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics…
The study of spatial symmetries was accomplished during the last century, and had greatly improved our understanding of the properties of solids. Nowadays, the symmetry data of any crystal can be readily extracted from standard…
Time series anomaly detection (TSAD) is becoming increasingly vital due to the rapid growth of time series data across various sectors. Anomalies in web service data, for example, can signal critical incidents such as system failures or…
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 to the field of financial time series primarily and as a method for…
Existing Transformer-based models for point cloud analysis suffer from quadratic complexity, leading to compromised point cloud resolution and information loss. In contrast, the newly proposed Mamba model, based on state space models (SSM),…
The ability to collect and analyze large amounts of data is a growing problem within the scientific community. The growing gap between data and users calls for innovative tools that address the challenges faced by big data volume, velocity…
DADApy is a python software package for analysing and characterising high-dimensional data manifolds. It provides methods for estimating the intrinsic dimension and the probability density, for performing density-based clustering and for…
By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…