Topological Data Visualization Workshop
The aim of this workshop is to discuss the application of topological techniques to visualizing large networks. Networks are widely used in modeling social, biological and technological systems and to capture relationships among individuals and entities. Understanding their structure is critical to many applications, including neuroscience, epidemiology, law enforcement, public policy and marketing.
This workshop will consist of tutorials and research talks on various topological visualization methods. Specifically, we will explore the development of methods that enable researchers to create and share compelling visualizations of networks for diverse audiences.
In addition, we will examine how the explanatory and persuasive power of visualization can be used to improve our communities. We will also discuss the importance of exposing students to these skills, which are often excluded from standard data analysis curricula.
Topics that will be covered include: Statistical Distributions, Stochastic Algorithms for Feature Extraction and Tracking; In-Situ Data Summary; Relationship Exploration; and Multi-Variable Relationship Visualization.
Statistical Distributions have been extensively studied and utilized in the visualization community for many years as an effective means of efficiently analyzing and visualizing large datasets. Recent developments have shown that statistical distributions can be applied to a wide variety of tasks, including feature identification, extraction and tracking; in-situ data summary; query-driven visualization; multi-variable relationship exploration; and more.
Stochastic Algorithms for the Identification and Tracking of Feature Features
The use of stochastic algorithms in the visualization community has greatly increased in the past few years. These methods enable the efficient analysis of large and complex data sets by identifying characteristic features that appear in specific regions of the data.
These methods have been successful in a number of applications, such as dimensionality reduction , shape discovery , and computer vision. However, they are still facing some limitations such as time-dependent data, noise and uncertainty, or the need to support emerging data types, such as ensembles or high-dimensional point clouds.
One of the most prominent topological data analysis (TDA) methods is Mapper. Compared to clustering, which focuses on the geometric features of the data points, Mapper is more concerned with their topological properties. In a nutshell, it can distinguish between data points that are uniformly spread over a certain area, such as a disk, from data points that are scattered around a circle or figure-eight shapes.
In addition to being able to detect topological structures, Mapper can also identify clusters of data points with a high concentration of some characteristics. For instance, it can identify clusters of poems composed by two Iranian poets, Ferdowsi and Hafez.
The resulting map can be visualized as a graph with nodes and edges representing data points. The size of the nodes can be regulated to correspond to the number of data points in each cluster and the edge lengths can be based on some chosen characteristics of the data, such as survival rates for breast cancer patients.
Despite their increasing popularity, topological data analysis methods are still facing some limitations such as time-dependent and noisy data, or the need to support emerging data types, e.g., ensemble data or high-dimensional point clouds. This workshop will seek to develop new computational and visual methods that can overcome these challenges by providing a framework for efficient and robust computation and visualizing of subtle structural patterns in multi-scale and time-varying data.