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Abstract:
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Finding "interesting" projections in high dimensional space has a long tradition, yielding in methodological solutions such as the grand tour (Asimov 1958) or projection pursuit methods. While the grand tour walks through the high-dimensional space on a path that covers all possible lower dimensional projections, this path is optimized in projection pursuit methods for one specific optimality index. We propose an application of graph-theoretic indices as optimization criterion in projection pursuit: instead of a single criterion, a combination of these indices allows us to look for projections that are e.g. 80% "skinny", 15% "clumpy" with 0% outliers, etc. By allowing to change the index setting interactively, the analyst can guide the projection pursuit in more ways than the usual parameters allow.
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