Dense rectangles in object-attribute data

We study dense rectangles in data tables with binary attributes, i.e. subtables which are “almost full of 1’s”. Dense rectangles represent interesting patterns which an be thought of as particular granules in data tables. Rectangles which are “full of 1’s” appear as natural patterns in several areas and have been widely studied in computer science and data analysis. Our paper presents a study in which we loosen the criterion of a density of a rectangle. Instead of rectangles full of 1’s, we are interested in rectangles which may contain a few 0’s. This way, one can capture different kinds of patterns in data. These patterns elude methods which extract only rectangles “full of 1’s”. We propose several ways to define density of a rectangle. We concentrate on column-like (and dually, row-like) conditions which say that a rectangle is dense if each of its columns contains at most a given (small) number of 0’s. For this case, we develop theoretical insight resembling that one behind rectangles “full of 1’s”, present illustrative examples and experiments, and outline further issues and future research.