Replacing full rectangles by dense rectangles: concept lattices and attribute implications

Maximal full rectangles in tabular data are useful in several areas of data engineering. This paper presents a survey of results in which we replace "full rectangles" by "dense rectangles". This way, we go from exact to approximate. We develop issues directly related to maximal dense rectangles: closure-like structures, concept lattices, attribute implications, a computationally tractable description of non-redundant bases of implications, and an algorithm for their computation. We present illustrative examples and results of experiments