While clustering is one of the most popular methods for data mining, analysts lack adequate tools for quick, iterative clustering analysis, which is essential for hypothesis generation and data reasoning. We introduce Clustrophile, an interactive tool for iteratively computing discrete and continuous data clusters, rapidly exploring different choices of clustering parameters, and reasoning about clustering instances in relation to data dimensions. Clustrophile combines three basic visualizations – a table of raw datasets, a scatter plot of planar projections, and a matrix diagram (heatmap) of discrete clusterings – through interaction and intermediate visual encoding. Clustrophile also contributes two spatial interaction techniques, forward projection and backward projection, and a visualization method, prolines, for reasoning about two-dimensional projections obtained through dimensionality reductions.