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

With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…

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…

Time-series classification (TSC) has advanced significantly with deep learning, yet most models rely solely on raw numerical inputs, overlooking alternative representations. While texture-based encodings such as Gramian Angular Fields (GAF)…

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…

Firm financials are well established as return predictors, being the inspiration for a large set of anomalies in the asset pricing literature. Employing topological data analysis we revisit the question of association between seven of the…

Unfamiliar or esoteric visual forms arise in many areas of visualization. While such forms can be intriguing, it can be unclear how to make effective use of them without long periods of practice or costly user studies. In this work we…

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…

Big Data involves both a large number of events but also many variables. This paper will concentrate on the challenge presented by the large number of variables in a Big Dataset. It will start with a brief review of exploratory data…

Many data sets, crucial for today's applications, consist essentially of enormous networks, containing millions or even billions of elements. Having the possibility of visualizing such networks is of paramount importance. We propose an…

The efficiency of modern computer graphics allows us to explore collections of space curves simultaneously with "drag-to-rotate" interfaces. This inspires us to replace "scatterplots of points" with "scatterplots of curves" to…

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…

Data Visualization has become an important aspect of big data analytics and has grown in sophistication and variety. We specifically identify the need for an analytical framework for data visualization with textual information. Data…

Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial…

Loss landscapes are a powerful tool for understanding neural network optimization and generalization, yet traditional low-dimensional analyses often miss complex topological features. We present Landscaper, an open-source Python package for…

Motivation: The visualization and analysis of high-dimensional data are essential in biomedical research. There is a need for secure, scalable, and reproducible tools to facilitate data exploration and interpretation. Results: We introduce…

Denoising diffusion probabilistic models are currently becoming the leading paradigm of generative modeling for many important data modalities. Being the most prevalent in the computer vision community, diffusion models have also recently…

Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…

This paper investigates new data exploration experiences that enable blind users to interact with statistical data visualizations$-$bar plots, heat maps, box plots, and scatter plots$-$leveraging multimodal data representations. In addition…

Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these…