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.Keywords Dimensionality reduction · mapping · solution quality · model selection 1 IntroductionThe problem of dimensionality reduction is core to statistics, machine learning, and visualization. High dimensional data can contain a large amount of noise and importantly for visualization, the human brain can only comprehend three dimensions. Thus, there is a need to reduce data into an interpretable format by converting high dimensional data into two or three dimensions, which can subsequently be visualized using a two or three dimensional scatterplot. To meet the need for dimensionality reduction methods, a plethora of algorithms and associated fitting methods have been developed. A researcher wishing to perform dimensionality reduction for visualization will be presented with a choice of hundreds of algorithms. Which algorithm should be used? This paper describes a visualization framework called QVisVis and associated software tools implemented in R to help choose dimensionality reduction methods, tune these methods, and visually evaluate the quality of dimensionality reduction solutions. The major contributions of these paper are to review and synthesize previous work on evaluating and "visualizing" performance metrics, create an overall visualization framework for "visualizing" visualization quality, and implement the framework in an R toolkit.