  Dimensionality reduction is often used as an initial step in data
exploration, either as preprocessing for classification or regression or for
visualization. Most dimensionality reduction techniques to date are
unsupervised; they do not take class labels into account (e.g., PCA, MDS,
t-SNE, Isomap). Such methods require large amounts of data and are often
sensitive to noise that may obfuscate important patterns in the data. Various
attempts at supervised dimensionality reduction methods that take into account
auxiliary annotations (e.g., class labels) have been successfully implemented
with goals of increased classification accuracy or improved data visualization.
Many of these supervised techniques incorporate labels in the loss function in
the form of similarity or dissimilarity matrices, thereby creating
over-emphasized separation between class clusters, which does not realistically
represent the local and global relationships in the data. In addition, these
approaches are often sensitive to parameter tuning, which may be difficult to
configure without an explicit quantitative notion of visual superiority. In
this paper, we describe a novel supervised visualization technique based on
random forest proximities and diffusion-based dimensionality reduction. We
show, both qualitatively and quantitatively, the advantages of our approach in
retaining local and global structures in data, while emphasizing important
variables in the low-dimensional embedding. Importantly, our approach is robust
to noise and parameter tuning, thus making it simple to use while producing
reliable visualizations for data exploration.
