相关论文: An Introduction to Topological Data Analysis Ball …

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 rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology,…

ViDaExpert is a tool for visualization and analysis of multidimensional vectorial data. ViDaExpert is able to work with data tables of "object-feature" type that might contain numerical feature values as well as textual labels for rows…

Projections, or dimensionality reduction methods, are techniques of choice for the visual exploration of high-dimensional data. Many such techniques exist, each one of them having a distinct visual signature - i.e., a recognizable way to…

Scatterplots are one of the simplest and most commonly-used visualizations for understanding quantitative, multidimensional data. However, since scatterplots only depict two attributes at a time, analysts often need to manually generate and…

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the…

We introduce FDApy, an open-source Python package for the analysis of functional data. The package provides tools for the representation of (multivariate) functional data defined on different dimensional domains and for functional data that…

Periodically occurring accumulations of events or measured values are present in many time-dependent datasets and can be of interest for analyses. The frequency of such periodic behavior is often not known in advance, making it difficult to…

Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…

Topological data analysis asks when balls in a metric space $(X,d)$ intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature.…

We introduce the idea of temporal graphs, a representation that encodes temporal data into graphs while fully retaining the temporal information of the original data. This representation lets us explore the dynamic temporal properties of…

Statistical tools are crucial for studying and modeling turbulent flows, where chaotic velocity fluctuations span a wide range of spatial and temporal scales. Advances in image velocimetry, especially in tracking-based methods, now allow…

Semantic map models visualize systematic relations among semantic functions through graph structures and are widely used in linguistic typology. However, existing construction methods either depend on labor-intensive expert reasoning or on…

Background: Over the last years, more and more biological data became available. Besides the pure amount of new data, also its dimensionality - the number of different attributes per data point - increased. Recently, especially the amount…

Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…

Two-dimensional data maps can visually reveal information about the relations between data instances. Popular techniques to construct data maps are t-SNE and UMAP. The resulting point-based visualizations, though, provide information only…

Charts and graphs help people analyze data, but can they also be useful to AI systems? To investigate this question, we perform a series of experiments with two commercial vision-language models: GPT 4.1 and Claude 3.5. Across three…

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…

Datamation is designed to animate an analysis pipeline step by step, which is an intuitive and effective way to interpret the results from data analysis. However, creating a datamation is not easy. A qualified datamation needs to not only…

Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological…