Axis contraction of parallel coordinates using spectral graph analysis

Parallel coordinates is well-known as a popular tool for visualizing the underlying relationships among variables in high-dimensional datasets. This visualization technique is useful for visually understanding the degree of correlation between data samples in terms of two adjacent axes. However, this representation still suffers from distracting visual clutter especially when the numbers of data samples and their associated dimension become high, because the associated polyline samples intricately overlap with each other within the limited screen space. This paper presents a method of alleviating such visual clutter by contracting multiple axes through the analysis of correlation between every pair of variables. In this method, we first define the similarity between a pair of dimensions as the value of the correlation coefficient, and construct a subgraph from the complete graph through eliminating all the edges in that their absolute correlation coefficients are less than some threshold, and then reorder the multiple axes by projecting the nodes onto the primary axis obtained using the spectral graph analysis. This allows us to compose a dendrogram tree by recursively merging a pair of the closest axes one by one. Smooth animation of the associated axis contraction and expansion has also been implemented to enhance the visual readability of behavior inherent in the given high-dimensional datasets. We also conducted a user study to investigate how the correlations among coordinate axes are better visualized using our approach.