Most data arrive with more than two numeric variables which means that plotting it on a computer screen or printed page presents a challenge: how do you visually explore for associations between more than two variables? Visualising data provides the opportunity to discover what we never expected, because it requires fewer assumptions to be made. Visualising elements of a model fit is a primary way to diagnose whether the fit matches this data. Two of more numeric variables is considered to be multivariate data, and when there are substantially more we would consider it to be high-dimensional data. This book provides you with the tools to visually explore high dimensions, to uncover associations, clustering and anomalies that may be missed when only using common methods for plotting one or two variables. It also illustrates how to use visualisation to understand how your model is operating on the data, to be able to explain how it is arriving at decisions. To make effective use of this material the reader should have a basic working knowledge of R and some understanding of multivariate statistical methods or machine learning methods. The book could form an independent course on visualization or be used as part of courses on multivariate statistical methods or machine learning.

High-dimensional data visualisation is valuable for understanding dimension reduction methods, unsupervised and supervised classification. This book is organised into these three topics, following overview and introductory chapters. The dimension reduction chapters cover principal component analysis and nonlinear dimension reduction. The chapters on cluster analysis cover hierarchical and k-means algorithms, model-based and self-organising maps, and finish with ways to communicate results and how to compare different results. The chapters on classification cover linear discriminant analysis, tree and forest algorithms, support vector machines and neural networks. We explain how to break down a neural network to examine the components, how to visualize predictive probabilities, and how to incorporate explainable AI metrics to develop a deeper understanding about how the model operates.

Dianne Cook and Ursula Laa have jointly published numerous papers on methodology for high-dimensional data visualisation in the past decade. This book is a result of these collaborations. Dianne Cook has been researching methods for data visualisation, particularly for exploratory data analysis, and data mining, for more than 30 years. She is a Distinguished Professor of Statistics at Monash University, Fellow of the American Statistical Association, past editor of the Journal of Computational and Graphical Statistics, and the R Journal, Board Member of the R Foundation, and elected member of the International Statistical Institute, and author of numerous R packages. Ursula Laa is an Assistant Professor at the Institute of Statistics of the University of Natural Resources and Life Sciences in Vienna. She works on new methods for the visualisation of multivariate data and models, and on interdisciplinary applications of statistics and data science methods in different fields.