Abstract
Two-dimensional space embeddings such as Multi-Dimensional Scaling (MDS) are a popular means to gain insight into high-dimensional data relationships. However, in all but the simplest cases these embeddings suffer from significant distortions, which can lead to misinterpretations of the high-dimensional data. These distortions occur both at the global inter-cluster and the local intra-cluster levels. The former leads to misinterpretation of the distances between the various N-D cluster populations, while the latter hampers the appreciation of their individual shapes and composition, which we call cluster appearance. The distortion of cluster appearance incurred in the 2-D embedding is unavoidable since such low-dimensional embeddings always come at the loss of some of the intra-cluster variance. In this paper, we propose techniques to overcome these limitations by conveying the N-D cluster appearance via a framework inspired by illustrative design. Here we make use of Scagnostics which offers a set of intuitive feature descriptors to describe the appearance of 2-D scatterplots. We extend the Scagnostics analysis to N-D and then devise and test via crowd-sourced user studies a set of parameterizable texture patterns that map to the various Scagnostics descriptors. Finally, we embed these N-D Scagnostics-informed texture patterns into shapes derived from N-D statistics to yield what we call Cluster Appearance Glyphs. We demonstrate our framework with a dataset acquired to analyze program execution times in file systems.
Highlights
The late Jim Cray [1] described data-driven science as the evolution from hypotheses to patterns, and the most interesting and useful data patterns involve many more than just two variables
We introduce the concept of Cluster Appearance Glyph, a family of illustrative textures that can graphically encode the three scagnostics measures assessed in N-D
We have presented a framework for pre-classified data that addresses the fact that low-dimensional (2-D) space embedding of high-dimensional data suffers from significant suppression of important cluster detail
Summary
The late Jim Cray [1] described data-driven science as the evolution from hypotheses to patterns, and the most interesting and useful data patterns involve many more than just two variables. Focusing on dimension 10, tuition, in the upper-right portion of the figure, we observe that, while USC-Viterbi is an expensive school, it ends up located to the left of the cheaper Texas A&M This is a well-known phenomenon because biplots use the two most dominant Principal Component (PCA) vectors as a basis and project both data and dimension vectors into it. The visualization only coveys the variance of the two major PCA vectors; the remaining unexplained variance leads to this distortion These types of distortions occur with any projective N-D to 2-D mapping, linear or non-linear, in all but the most trivial cases. They affect individual point-pair relations as well as overall cluster appearance, such as density, composition, shape, and organization
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