Reliability of dimension reduction visualizations of hierarchical structures

Dimension reduction can produce visualizations of hierarchical structures, like those produced by cluster analysis. So far, reliability of such visualizations has only been assessed with rudimentary means. Here, a method for assessing reliability of such visualizations is developed. It measures how accurately the location of a data point in high-dimensional hierarchy tree can be inferred from a tree based on the low-dimensional visualization. The criterion can be used in point-wise fashion, allowing visual assessment of results, or as average values, for comparing visualizations. Use of the criterion is demonstrated on handwritten digits data, comparing visualizations by three dimension reduction methods.