Related papers: An Introduction to Topological Data Analysis Ball …

Tables form a central component in both exploratory data analysis and formal reporting procedures across many industries. These tables are often complex in their conceptual structure and in the computations that generate their individual…

The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…

Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…

Developing Machine Learning (ML) algorithms for heterogeneous/mixed data is a longstanding problem. Many ML algorithms are not applicable to mixed data, which include numeric and non-numeric data, text, graphs and so on to generate…

While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…

The Big Data landscape poses challenges in managing diverse data formats, requiring efficient storage and processing for high-quality analysis. Effective metadata management is crucial for organizing, accessing, and reusing data within…

We identify two major steps in data analysis, data exploration for understanding and observing patterns/relationships in data; and construction, design and assessment of various models to formalize these relationships. For each step, there…

Astronomical researchers often think of analysis and visualization as separate tasks. In the case of high-dimensional data sets, though, interactive exploratory data visualization can give far more insight than an approach where data…

Large Language Models (LLMs) are a powerful tool for statistical text analysis, with derived sequences of next-token probability distributions offering a wealth of information. Extracting this signal typically relies on metrics such as…

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…

Nonlinear dimension reduction (NLDR) techniques such as tSNE, and UMAP provide a low-dimensional representation of high-dimensional data ($p\text{-}D$) by applying a nonlinear transformation. NLDR often exaggerates random patterns. But NLDR…

Following the seminal idea of Tukey, data depth is a function that measures how close an arbitrary point of the space is located to an implicitly defined center of a data cloud. Having undergone theoretical and computational developments,…

We use the notion of topological data analysis to compare metrics on data sets. We provide two different motivating examples for this. The first of these is a point cloud data set that has $\mathbb{R}^2$ as its ambient space, and is…

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.…

The rootogram is a graphical tool associated with the work of J. W. Tukey that was originally used for assessing goodness of fit of univariate distributions. Here we extend the rootogram to regression models and show that this is…

The growth of computational astrophysics and complexity of multidimensional datasets evidences the need for new versatile visualization tools for both analysis and presentation of the data. In this work we show how to use the open source…

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)…

There is a growing need for unbiased clustering methods, ideally automated. We have developed a topology-based analysis tool called Two-Tier Mapper (TTMap) to detect subgroups in global gene expression datasets and identify their…

Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…

Machine learning algorithms using deep architectures have been able to implement increasingly powerful and successful models. However, they also become increasingly more complex, more difficult to comprehend and easier to fool. So far, most…