Visualizing data through curvilinear representations of matrices

Most high dimensional data visualization techniques embed or project the data onto a low dimensional space which is then used for viewing. Results are thus limited by how much of the information in the data can be conveyed in two or three dimensions. Methods1are described for a lossless functional representation of any real matrix that can capture key features of the data, such as distances and correlations. This approach can be used to visualize both subjects and variables as curves, allowing one to see patterns of subjects, patterns of variables, and how the subject and variable patterns relate to one another. A theoretical justification is provided for this approach, and various facets of the method's usefulness are illustrated on both synthetic and real data sets.