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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]

Multivariate data is often visualized using linear projections, produced by techniques such as principal component analysis, linear discriminant analysis, and projection pursuit. A problem with projections is that they obscure low and high density regions near the center of the distribution. Sections, or slices, can help to reveal them. This article develops a section pursuit method, building on the extensive work in projection pursuit, to search for interesting slices of the data. Linear projections are used to define sections of the parameter space, and to calculate interestingness by comparing the distribution of observations, inside and outside a section. By optimizing this index, it is possible to reveal features such as holes (low density) or grains (high density). The optimization is incorporated into a guided tour so that the search for structure can be dynamic. The approach can be useful for problems when data distributions depart from uniform or normal, as in visually exploring nonlinear manifolds, and functions in multivariate space. Two applications of section pursuit are shown: exploring decision boundaries from classification models, and exploring subspaces induced by complex inequality conditions from a multiple parameter model. The new methods are available in R, in the tourr package. for this article are available online. [ABSTRACT FROM AUTHOR]

In high-dimensional data analysis, the curse of dimensionality reasons that points tend to be far away from the center of the distribution and on the edge of high-dimensional space. Contrary to this, is that projected data tends to clump at the center. This gives a sense that any structure near the center of the projection is obscured, whether this is true or not. A geometric transformation to reverse the curse, is defined in this article, which uses radial transformations on the projected data. It is integrated seamlessly into the grand tour algorithm, and we have called it a burning sage tour, to indicate that it reverses the curse. The work is implemented into the tourr package in R. Several case studies are included that show how the sage visualizations enhance exploratory clustering and classification problems. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

AbstractIndexes are useful for summarizing multivariate information into single metrics for monitoring, communicating, and decision-making. While most work has focused on defining new indexes for specific purposes, more attention needs to be directed towards making it possible to understand index behavior in different data conditions, and to determine how their structure affects their values and the variability therein. Here we discuss a modular data pipeline recommendation to assemble indexes. It is universally applicable to index computation and allows investigation of index behavior as part of the development procedure. One can compute indexes with different parameter choices, adjust steps in the index definition by adding, removing, and swapping them to experiment with various index designs, calculate uncertainty measures, and assess indexes’ robustness. The paper presents three examples to illustrate the usage of the pipeline framework: comparison of two different indexes designed to monitor the spatio-temporal distribution of drought in Queensland, Australia; the effect of dimension reduction choices on the Global Gender Gap Index (GGGI) on countries’ ranking; and how to calculate bootstrap confidence intervals for the Standardized Precipitation Index (SPI). The methods are supported by a new R package, called tidyindex. Supplemental materials for the article are available online. [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]

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]