  Principal component analysis is a long-standing go-to method for exploring
multivariate data. The principal components are linear combinations of the
original variables, ordered by descending variance. The first few components
typically provide a good visual summary of the data. Tours also make linear
projections of the original variables but offer many different views, like
examining the data from different directions. The grand tour shows a smooth
sequence of projections as an animation following interpolations between random
target bases. The manual radial tour rotates the selected variable's
contribution into and out of a projection. This allows the importance of the
variable to structure in the projection to be assessed. This work describes a
mixed-design user study evaluating the radial tour's efficacy compared with
principal component analysis and the grand tour. A supervised classification
task is assigned to participants who evaluate variable attribution of the
separation between two classes. Their accuracy in assigning the variable
importance is measured across various factors. Data were collected from 108
crowdsourced participants, who performed two trials with each visual for 648
trials in total. Mixed model regression finds strong evidence that the radial
tour results in a large increase in accuracy over the alternatives.
Participants also reported a preference for the radial tour in comparison to
the other two methods.
