Scaling Invariant Multidimensional Projections for Visualization

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Finding good projections from multi-dimensional data domains to the 2D screen is a standard problem in many fields. Multidimensional data usually considered in Multifield Visualization (a subfield of Scientific Visualization) often comes with the property that the dimensions are measured in different physical units, making the ratio between arbitrary. We propose to develop projection techniques that are independent of the chosen physical unit of each dimension, i.e., they are invariant on the scaling of each dimension. While many standard measures and features do not have this scaling invariance (such as relative Euclidean distance, PCA, t-SNE), simple solutions like normalization of each dimension does not solve the problem adequately. We propose to develop scaling invariant versions of standard automatic non-linear projection techniques such as t-SNE. Also, we search for scaling invariant versions of linear projections (such as PCA), as well as for standard clustering techniques.We see the main application of scaling invariant projection techniques in the visual analysis of multifield data.