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This article describes new user controls for examining high-dimensional data using low-dimensional linear projections and slices. A user can interactively change the contribution of a given variable to a low-dimensional projection, which is useful for exploring the sensitivity of structure to particular variables. The user can also interactively shift the center of a slice, for example, to explore how structure changes in local subspaces. The Mathematica package as well as example notebooks are provided, which contain functions enabling the user to experiment with these new manual controls, with one specifically for exploring regions and boundaries produced by classification models. The advantage of Mathematica is its linear algebra capabilities and interactive cursor location controls. Some limited implementation has also been made available in the R package tourr. for this article are available online. [ABSTRACT FROM AUTHOR]

This article discusses a high‐dimensional visualization technique called the tour, which can be used to view data in more than three dimensions. We review the theory and history behind the technique, as well as modern software developments and applications of the tour that are being found across the sciences and machine learning. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional DataStatistical and Graphical Methods of Data Analysis > Statistical Graphics and VisualizationStatistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis [ABSTRACT FROM AUTHOR]

A guided tour helps to visualise high-dimensional data by showing low-dimensional projections along a projection pursuit optimisation path. Projection pursuit is a generalisation of principal component analysis in the sense that different indexes are used to define the interestingness of the projected data. While much work has been done in developing new indexes in the literature, less has been done on understanding the optimisation. Index functions can be noisy, might have multiple local maxima as well as an optimal maximum, and are constrained to generate orthonormal projection frames, which complicates the optimization. In addition, projection pursuit is primarily used for exploratory data analysis, and finding the local maxima is also useful. The guided tour is especially useful for exploration because it conducts geodesic interpolation connecting steps in the optimisation and shows how the projected data changes as a maxima is approached. This work provides new visual diagnostics for examining a choice of optimisation procedure based on the provision of a new data object which collects information throughout the optimisation. It has helped to diagnose and fix several problems with projection pursuit guided tour. This work might be useful more broadly for diagnosing optimisers and comparing their performance. The diagnostics are implemented in the R package ferrn. [ABSTRACT FROM AUTHOR]

Projection pursuit is used to find interesting low-dimensional projections of high-dimensional data by optimizing an index over all possible projections. Most indexes have been developed to detect departure from known distributions, such as normality, or to find separations between known groups. Here, we are interested in finding projections revealing potentially complex bivariate patterns, using new indexes constructed from scagnostics and a maximum information coefficient, with a purpose to detect unusual relationships between model parameters describing physics phenomena. The performance of these indexes is examined with respect to ideal behaviour, using simulated data, and then applied to problems from gravitational wave astronomy. The implementation builds upon the projection pursuit tools available in the R package, tourr, with indexes constructed from code in the R packages, binostics, minerva and mbgraphic. [ABSTRACT FROM AUTHOR]

Taking projections of high-dimensional data is a common analytical and visualization technique in statistics for working with high-dimensional problems. Sectioning, or slicing, through high dimensions is less common, but can be useful for visualizing data with concavities, or nonlinear structure. It is associated with conditional distributions in statistics, and also linked brushing between plots in interactive data visualization. This short technical note describes a simple approach for slicing in the orthogonal space of projections obtained when running a tour, thus presenting the viewer with an interpolated sequence of sliced projections. The method has been implemented in R as an extension to the tourr package, and can be used to explore for concave and nonlinear structures in multivariate distributions. for this article are available online. [ABSTRACT FROM AUTHOR]

The tourr package in R has several algorithms and displays for showing multivariate data as a sequence of low-dimensional projections. It can display as a movie but has no capacity for interaction, such as stop/go, change tour type, drop/add variables. The tourrGui package provides these sorts of controls, but the interface is programmed with the dated RGtk2 package. This work explores using custom messages to pass data from R to D3 for viewing, using the Shiny framework. This is an approach that can be generally used for creating all sorts of interactive graphics. [ABSTRACT FROM AUTHOR]