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 nonredundant bases of implications, and an algorithm for their computation. We present illustrative examples and results of experiments. I. PROBLEM SETTING Data tables describing objects (table rows), attributes (table columns) and their relationship (table entry is × or blank depending on whether an object has or does not have an attribute) belong to fundamental means of data representation. An example is presented

• Type: Conference
• Year: 2006
• Where: IRI
• Authors: Radim Belohlávek, Vilém Vychodil
• Keywords: Dense Rectangles, Full Rectangles, Information Retrieval, IRI 2006, Maximal Dense