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

Data visualizations like charts are fundamental tools for quantitative analysis and decision-making across fields, requiring accurate interpretation and mathematical reasoning. The emergence of Multimodal Large Language Models (MLLMs)…

We present ShapeVis, a scalable visualization technique for point cloud data inspired from topological data analysis. Our method captures the underlying geometric and topological structure of the data in a compressed graphical…

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,…

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…

Simulated high-dimensional data is useful for testing, validating, and improving algorithms used in dimension reduction, supervised and unsupervised learning. High-dimensional data is characterized by multiple variables that are dependent…

Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming…

Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…

Visualization of multidimensional, categorical data is a common challenge across scientific areas and, in particular, the life sciences. The goal is to create a comprehensive overview of the underlying data which allows to assess multiple…

Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…

Cartogram drawing is a technique for showing geography-related statistical information, such as demographic and epidemiological data. The idea is to distort a map by resizing its regions according to a statistical parameter by keeping the…

The rapid development of modern technology facilitates the appearance of numerous unprecedented complex data which do not satisfy the axioms of Euclidean geometry, while most of the statistical hypothesis tests are available in Euclidean 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…

This paper gives a review and synthesis of methods of evaluating dimensionality reduction techniques. Particular attention is paid to rank-order neighborhood evaluation metrics. A framework is created for exploring dimensionality reduction…

Simultaneous Localization and Mapping (SLAM) is considered an ever-evolving problem due to its usage in many applications. Evaluation of SLAM is done typically using publicly available datasets which are increasing in number and the level…

This paper introduces topological data analysis. Starting from notions of a metric space and some elementary graph theory, we take example sets of data and demonstrate some of their topological properties. We discuss simplicial complexes…

Background: Current nomogram can only be created for regression algorithm. Providing nomogram for any machine learning (ML) algorithms may accelerate model deployment in clinical settings or improve model availability. We developed an R…

Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…

There is heightened interest in quantum algorithms for Topological Data Analysis (TDA) as it is a powerful tool for data analysis, but it can get highly computationally expensive. Even though there are different propositions and…

Analyzing flight trajectory data sets poses challenges due to the intricate interconnections among various factors and the high dimensionality of the data. Topological Data Analysis (TDA) is a way of analyzing big data sets focusing on the…

Visual robot navigation within large-scale, semi-structured environments deals with various challenges such as computation intensive path planning algorithms or insufficient knowledge about traversable spaces. Moreover, many…