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AbstractRegression experts consistently recommend plotting residuals for model diagnosis, despite the availability of many numerical hypothesis test procedures designed to use residuals to assess problems with a model fit. Here we provide evidence for why this is good advice using data from a visual inference experiment. We show how conventional tests are too sensitive, which means that too often the conclusion would be that the model fit is inadequate. The experiment uses the lineup protocol which puts a residual plot in the context of null plots. This helps generate reliable and consistent reading of residual plots for better model diagnosis. It can also help in an obverse situation where a conventional test would fail to detect a problem with a model due to contaminated data. The lineup protocol also detects a range of departures from good residuals simultaneously. Supplemental materials for the 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]

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]

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]

Calendars are broadly used in society to display temporal information and events. This article describes a new calendar display for plotting data that include a layout algorithm with many options, and faceting functionality. The functions use modular arithmetic on the date variable to restructure the data into a calendar format. The user can apply the grammar of graphics to create plots inside each calendar cell, and thus the displays synchronize neatly with ggplot2 graphics. The motivating application is studying pedestrian behavior in Melbourne, Australia, based on counts which are captured at hourly intervals by sensors scattered around the city. Faceting by the usual features such as day and month is insufficient to examine the behavior. Making displays on a monthly calendar format helps to understand pedestrian patterns relative to events such as work days, weekends, holidays, and special events. The functions for the calendar algorithm are available in the R package sugrrants. for this article are available online. [ABSTRACT FROM AUTHOR]

Graphics play a crucial role in statistical analysis and data mining. Being able to quantify structure in data that is visible in plots, and how people read the structure from plots is an ongoing challenge. The lineup protocol provides a formal framework for data plots, making inference possible. The data plot is treated like a test statistic, and lineup protocol acts like a comparison with the sampling distribution of the nulls. This article describes metrics for describing structure in data plots and evaluates them in relation to the choices that human readers made during several large Amazon Turk studies using lineups. The metrics that were more specific to the plot types tended to better match subject choices, than generic metrics. The process that we followed to evaluate metrics will be useful for general development of numerically measuring structure in plots, and also in future experiments on lineups for choosing blocks of pictures. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Temporal data are information measured in the context of time. This contextual structure provides components that need to be explored to understand the data and that can form the basis of interactions applied to the plots. In multivariate time series, we expect to see temporal dependence, long term and seasonal trends, and cross-correlations. In longitudinal data, we also expect within and between subject dependence. Time series and longitudinal data, although analyzed differently, are often plotted using similar displays. We provide a taxonomy of interactions on plots that can enable exploring temporal components of these data types, and describe how to build these interactions using data transformations. Because temporal data are often accompanied other types of data we also describe how to link the temporal plots with other displays of data. The ideas are conceptualized into a data pipeline for temporal data and implemented into the R packagecranvas. This package provides many different types of interactive graphics that can be used together to explore data or diagnose a model fit. [ABSTRACT FROM AUTHOR]

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]

Deconstructing a time index into time granularities can assist in exploration and automated analysis of large temporal datasets. This article describes classes of time deconstructions using linear and cyclic time granularities. Linear granularities respect the linear progression of time such as hours, days, weeks and months. Cyclic granularities can be circular such as hour-of-the-day, quasi-circular such as day-of-the-month, and aperiodic such as public holidays. The hierarchical structure of granularities creates a nested ordering: hour-of-the-day and second-of-the-minute are single-order-up. Hour-of-the-week is multiple-order-up, because it passes over day-of-the-week. Methods are provided for creating all possible granularities for a time index. A recommendation algorithm provides an indication whether a pair of granularities can be meaningfully examined together (a "harmony"), or when they cannot (a "clash"). Time granularities can be used to create data visualizations to explore for periodicities, associations and anomalies. The granularities form categorical variables (ordered or unordered) which induce groupings of the observations. Assuming a numeric response variable, the resulting graphics are then displays of distributions compared across combinations of categorical variables. The methods implemented in the open source R package gravitas are consistent with a tidy workflow, with probability distributions examined using the range of graphics available in ggplot2. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

Statistical inference provides the protocols for conducting rigorous science, but data plots provide the opportunity to discover the unexpected. These disparate endeavours are bridged by visual inference, where a lineup protocol can be employed for statistical testing. Human observers are needed to assess the lineups, typically using a crowd‐sourcing service. This paper describes a new approach for computing statistical significance associated with the results from applying a lineup protocol. It utilizes a Dirichlet distribution to accommodate different levels of visual interest in individual null panels. The suggested procedures facilitate statistical inference for a broader range of data problems. [ABSTRACT FROM AUTHOR]

AbstractThe usual goal of supervised learning is to find the best model, the one that optimizes a particular performance measure. However, what if the explanation provided by this model is completely different from another model and different again from another model despite all having similarly good fit statistics? Is it possible that the equally effective models put the spotlight on different relationships in the data? Inspired by Anscombe’s quartet, this article introduces a Rashomon Quartet, that is a set of four models built on a synthetic dataset which have practically identical predictive performance. However, the visual exploration reveals distinct explanations of the relations in the data. This illustrative example aims to encourage the use of methods for model visualization to compare predictive models beyond their performance. [ABSTRACT FROM AUTHOR]

Statistical inference provides the protocols for conducting rigorous science, but data plots provide the opportunity to discover the unexpected. These disparate endeavours are bridged by visual inference, where a lineup protocol can be employed for statistical testing. Human observers are needed to assess the lineups, typically using a crowd-sourcing service. This paper describes a new approach for computing statistical significance associated with the results from applying a lineup protocol. It utilizes a Dirichlet distribution to accommodate different levels of visual interest in individual null panels. The suggested procedures facilitate statistical inference for a broader range of data problems. [ABSTRACT FROM AUTHOR]

Background: Despite the availability of many ready-made testing software, reliable detection of differentially expressed genes in RNA-seq data is not a trivial task. Even though the data collection is considered high-throughput, data analysis has intricacies that require careful human attention. Researchers should use modern data analysis techniques that incorporate visual feedback to verify the appropriateness of their models. While some RNA-seq packages provide static visualization tools, their capabilities should be expanded and their meaningfulness should be explicitly demonstrated to users. Results: In this paper, we 1) introduce new interactive RNA-seq visualization tools, 2) compile a collection of examples that demonstrate to biologists why visualization should be an integral component of differential expression analysis. We use public RNA-seq datasets to show that our new visualization tools can detect normalization issues, differential expression designation problems, and common analysis errors. We also show that our new visualization tools can identify genes of interest in ways undetectable with models. Our R package "bigPint" includes the plotting tools introduced in this paper, many of which are unique additions to what is currently available. The "bigPint" website is located at https://lindsayrutter.github.io/bigPint and contains short vignette articles that introduce new users to our package, all written in reproducible code. Conclusions: We emphasize that interactive graphics should be an indispensable component of modern RNA-seq analysis, which is currently not the case. This paper and its corresponding software aim to persuade 1) users to slightly modify their differential expression analyses by incorporating statistical graphics into their usual analysis pipelines, 2) developers to create additional complex and interactive plotting methods for RNA-seq data, possibly using lessons learned from our open-source codes. We hope our work will serve a small part in upgrading the RNA-seq analysis world into one that more wholistically extracts biological information using both models and visuals. [ABSTRACT FROM AUTHOR]