"Visualizing High-Dimensional Data and Dimensionality Reduction"

Abstract

High-dimensional data is ubiquitous today and used in various domains from insurance fraud detection to biology. For the explorative analysis of such data, visualization is an important tool. Living in a three-dimensional world, we as humans have a hard time imagining four or five dimensions, let alone hundreds of dimensions. So how do we visualize such data and what do we have to consider when doing so. In this lecture, we will first discuss the basics for visualizing multi- and high-dimensional data and dimensionality reduction to do so. We will explore different dimensionality reduction techniques, their purpose, strengths and weaknesses, and when to use them. When reducing the dimensionality for data visualization, often reducing hundreds of dimensions to just two for display on screen, it is inevitable that information is lost. Without knowing how the data looks in the high-dimensional space it is hard to know which information is lost. In the second part of this lecture, we will put particular emphasis on how to improve the interpretability of visualizations of dimensionality reduced data. In particular, we will have a look at how we can improve non-linear dimensionality reduction, for example by adding back some of the lost information or adapting them to specialized domain needs.