Visual discovery in multivariate binary data

This paper presents the concept of Monotone Boolean Function Visual Analytics (MBFVA) and its application to the medical domain. The medical application is concerned with discovering breast cancer diagnostic rules (i) interactively with a radiologist, (ii) analytically with data mining algorithms, and (iii) visually. The coordinated visualization of these rules opens an opportunity to coordinate the rules, and to come up with rules that are meaningful for the expert in the field, and are confirmed with the database. This paper shows how to represent and visualize binary multivariate data in 2-D and 3-D. This representation preserves the structural relations that exist in multivariate data. It creates a new opportunity to guide the visual discovery of unknown patterns in the data. In particular, the structural representation allows us to convert a complex border between the patterns in multidimensional space into visual 2-D and 3-D forms. This decreases the information overload on the user. The visualization shows not only the border between classes, but also shows a location of the case of interest relative to the border between the patterns. A user does not need to see the thousands of previous cases that have been used to build a border between the patterns. If the abnormal case is deeply inside in the abnormal area, far away from the border between "normal" and "abnormal" patterns, then this shows that this case is very abnormal and needs immediate attention. The paper concludes with the outline of the scaling of the algorithm for the large data sets.