Selection of Proximity Measures for Matrix Visualization of Binary Data

Exploratory data analysis (EDA: Tukey, 1977) has been introduced and extensively used for more than 30 years yet boxplot and scatterplot are still the major EDA tools for visualizing continuous data in the 21st century. On the other hand, multiple correspondence analysis (MCA) type of methods and mosaic plots are most popular in practice for visualizing multivariate binary and nominal data. But all these methods loose their efficiency when data dimensionality gets really high (hundreds/thousands), particularly when data is of non-continuous nature. Matrix visualization (MV) instead can simultaneously explore the associations of up to thousands of variables, subjects, and their interactions, without reducing dimension. MV permutes rows and columns of the raw data matrix together with two corresponding proximity matrices by suitable seriation (reordering) algorithms. These permuted matrices are then displayed as matrix maps through suitable color spectra for extracting the subject-clusters, variable-groups, and the subjects/variables interaction patterns. For binary data, conventional visualization techniques (boxplot, scatterplot (matrix), mosaic display, parallel coordinate plot, etc.) basically cannot provide users much visual information while the binary generalized association plots (bGAP), by integrating matrix visualization with suitably chosen proximity for binary data, can effectively present complex patterns for thousands of binary variables for thousands of subjects in one matrix visualization.