  A number of visual quality measures have been introduced in visual analytics
literature in order to automatically select the best views of high dimensional
data from a large number of candidate data projections. These methods generally
concentrate on the interpretability of the visualization and pay little
attention to the interpretability of the projection axes. In this paper, we
argue that interpretability of the visualizations and the feature
transformation functions are both crucial for visual exploration of high
dimensional labeled data. We present a two-part user study to examine these two
related but orthogonal aspects of interpretability. We first study how humans
judge the quality of 2D scatterplots of various datasets with varying number of
classes and provide comparisons with ten automated measures, including a number
of visual quality measures and related measures from various machine learning
fields. We then investigate how the user perception on interpretability of
mathematical expressions relate to various automated measures of complexity
that can be used to characterize data projection functions. We conclude with a
discussion of how automated measures of visual and semantic interpretability of
data projections can be used together for exploratory analysis in
classification tasks.
