Data compression is a powerful solution for addressing big data challenges in database and data management. In scientific data compression for vector fields, preserving topological information is essential for accurate analysis and visualization. The topological skeleton, a fundamental component of vector field topology, consists of critical points and their connectivity (i.e., separatrices). While previous work has focused on preserving critical points in error-controlled lossy compression, little attention has been given to preserving separatrices, which are equally important. In this work, we introduce TspSZ, an efficient error-bounded lossy compression framework designed to preserve both critical points and separatrices. Our key contributions are threefold. First, we propose TspSZ, a topological-skeleton-preserving lossy compression framework that integrates two algorithms, enabling existing critical-point-preserving compressors to also retain separatrices, significantly enhancing their topology preservation capabilities. Second, we optimize TspSZ for efficiency through tailored improvements and parallelization. Specifically, we introduce a new error control mechanism to achieve high compression ratios and implement a shared-memory parallelization strategy to boost compression throughput. Third, we evaluate TspSZ against state-of-the-art lossy and lossless compressors using four real-world scientific datasets. Experimental results show that TspSZ achieves compression ratios of up to 7.7× while effectively preserving the topological skeleton, ensuring efficient storage and transmission of scientific data without compromising topological integrity.

The complexity of large real-world graphs makes their analyses prohibitively costly and their visualizations uninformative. The idea behind graph reduction is to reduce the size of a graph while preserving its properties of interest. To improve computational efficiency and to provide provable guarantees, many graph reduction techniques employ randomization. However, the uncertainty associated with randomized graph reduction and its subsequent interpretation has remained largely unexplored. In this paper, we present a framework to quantify and visualize the uncertainty associated with randomized graph reduction techniques. We focus on spectral clustering introduced by Ng, Jordan, and Weiss, a popular graph reduction technique that reduces the number of nodes by clustering the nodes of a graph into super-nodes. We introduce two uncertainty measures – local adjusted Rand indices and co-occurrences – to quantify and visualize uncertainty associated with an ensemble of reduced graphs. We demonstrate via experiments, that these measures complement each other in visualizing uncertainty and guiding the selection of optimal numbers of clusters.

Machine learning algorithms have been used for predicting different risks – financial, medical, and legal – and have been argued to perform more efficiently than human experts. However, this exclusive focus on accuracy can be at the cost of the algorithms discriminating against people due to their age, gender, or race, since accuracy could work in opposition to equity. The challenge is that equity and fairness are innately human values that evolve as societies evolve, making it hard to represent them mathematically. Therefore, we propose a framework for including less biased human experts in the algorithm’s prediction loop to improve equity and maintain accuracy. In two field studies, one in the legal domain and the other in credit risk, we utilize publicly available datasets to obtain baseline measures of fairness. Subsequently, we obtain human input, which are used to debias the algorithm. Utilizing less biased human experts, as well as providing transparent and explainable predictions, will help increase legal compliance and the trust of various stakeholders in an organization.

The mapper construction is a widely used tool from topological data analysis in obtaining topological summaries of large, high-dimensional point cloud data. It has enjoyed great success in data science, including cancer research, sports analytics, and visualization. However, developing practical and automatic parameter selection for the mapper construction remains a challenging open problem for both the topological analysis and visualization communities. In this paper, we focus on parameter selection for the 1-dimensional skeleton of the mapper construction, called the mapper graph. Specifically, we explore how information criteria used in the X-means clustering algorithm can inform and generate adaptive covers for mapper graphs. Our approach thus makes novel progress towards automatic parameter selection for the mapper construction using information theory.

Word vector embeddings have been shown to contain and amplify biases in data they are extracted from. Consequently, many techniques have been proposed to identify, mitigate, and attenuate these biases in word representations. In this tutorial, we will review a collection of state-of-the-art debiasing techniques. To aid this, we provide an open source web-based visualization tool and offer hands-on experience in exploring the effects of these debiasing techniques on the geometry of high-dimensional word vectors. To help understand how various debiasing techniques change the underlying geometry, we decompose each technique into interpretable sequences of primitive operations, and study their effect on the word vectors using dimensionality reduction and interactive visual exploration.

In this paper, we present a measure associated with detection and inference of statistically anomalous clusters of a graph based on the likelihood test of observed and expected edges in a subgraph.This measure is adapted from spatial scan statistics for point sets and provides quantitative assessment for clusters.We discuss some important properties of this statistic and its relation to modularity and Bregman divergences.We apply a simple clustering algorithm to find clusters with large values of this measure in a variety of real-world data sets, and we illustrate its ability to identify statistically significant clusters of selected granularity.