  This paper gives a review and synthesis of methods of evaluating
dimensionality reduction techniques. Particular attention is paid to rank-order
neighborhood evaluation metrics. A framework is created for exploring
dimensionality reduction quality through visualization. An associated toolkit
is implemented in R. The toolkit includes scatter plots, heat maps, loess
smoothing, and performance lift diagrams. The overall rationale is to help
researchers compare dimensionality reduction techniques and use visual insights
to help select and improve techniques. Examples are given for dimensionality
reduction of manifolds and for the dimensionality reduction applied to a
consumer survey dataset.
