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

The Topological Data Analysis Ball Mapper (TDABM) algorithm of Dlotko (2019) provides a model free means to visualize multi-dimensional data. The visualizations are abstract two-dimensional representations of covers of the dataset. To…

Topological Data Analysis Ball Mapper (TDABM) offers a model-free visualization of multivariate data which does not necessitate the information loss associated with dimensionality reduction. TDABM Dlotko (2019) produces a cover of a…

Finance is heavily influenced by data-driven decision-making. Meanwhile, our ability to comprehend the full informational content of data sets remains impeded by the tools we apply in analysis, especially where the data is high-dimensional.…

The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…

Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper algorithm} and \emph{persistent homology}. In this paper we introduce new…

Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar-valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to…

The chemical sciences are producing an unprecedented amount of large, high-dimensional data sets containing chemical structures and associated properties. However, there are currently no algorithms to visualize such data while preserving…

In multiclass classification of multidimensional data, the user wants to build a model of the classes to predict the label of unseen data. The model is trained on the data and tested on unseen data with known labels to evaluate its quality.…

Software libraries for Topological Data Analysis (TDA) offer limited support for interactive visualization. Most libraries only allow to visualize topological descriptors (e.g., persistence diagrams), and lose the connection with the…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

Mapper is an algorithm that summarizes the topological information contained in a dataset and provides an insightful visualization. It takes as input a point cloud which is possibly high-dimensional, a filter function on it and an open…

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…

Current research provides methods to communicate uncertainty and adapts classical algorithms of the visualization pipeline to take the uncertainty into account. Various existing visualization frameworks include methods to present uncertain…

Unsupervised data representation and visualization using tools from topology is an active and growing field of Topological Data Analysis (TDA) and data science. Its most prominent line of work is based on the so-called Mapper graph, which…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

Scatterplots are a common tool for exploring multidimensional datasets, especially in the form of scatterplot matrices (SPLOMs). However, scatterplots suffer from overplotting when categorical variables are mapped to one or two axes, or the…

Topological Data Analysis (TDA) is a novel, and relatively new approach to analysing high-dimensional data sets. It does this by focussing on global properties like the shape and connectivity of the data giving it a significant advantage…

Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…

The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a…

Dataframes are a popular abstraction to represent, prepare, and analyze data. Despite the remarkable success of dataframe libraries in Rand Python, dataframes face performance issues even on moderately large datasets. Moreover, there is…