U-maps: topograpic visualization techniques for projections of high dimensional data (original) (raw)
The visualization of distance structures in high dimensional data as topographic maps (U-matrix) is a standard method for Emergent Self Organizing Maps (ESOM). This work describes the extension of this visualization to other projections like principal component analysis (PCA), independent component analysis (ICA), multidimensional scaling (MDS), Sammon's mapping, or Isomap. Each of the methods optimize different criteria in the projection to a low dimensional space that are desirable in certain applications. The results are commonly displayed as two-dimensional scatterplots. This visualization does not indicate if and where the mapping is folded, i.e. where the projected distances are displayed compressed compared to the original distances. The U-map technique presented here visualizes the original high-dimensional distances in the low-dimensional projection space using 3-dimensional landscapes. These landscapes can be explored using the paradigm of topograpic maps. High ridges indicate foldings of the projections. The added value of the U-map visualization technique for low dimensional projections is demonstrated using various synthetic and real data sets.
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