The Barycenter Heuristic and the Reorderable Matrix

Bertin’s reorderable matrix (Bertin 1981, 1983, 2001) is a simple visualization method for exploring tabular data. The basic idea is to transform a multidimensional data set into a 2D interactive graphic. The graphical presentation of a data set contains rows and columns which can be permuted, allowing different views of the data set. The actual data values are replaced with symbols, say circles or rectangles, that have a size relative to the actual data value. Processing the reorderable matrix involves bringing together similar rows and columns. The reorderable matrix suits well in application areas which call for human expertise to guide the automatic process, as in architecture (Adams & Daru, 1994; Veenendaal, 1994) and system analysis and project management (Ulrich & Eppinger, 1999) where the knowledge is difficult to transform into a form “understandable” for computers. When using the reorderable matrix, the manual and automatic phases for reordering the matrix take turns and support each others. Hence, the human knowledge guides the systems but the dull parts are left to computer. There are some known implementations for automatic reordering of the reorderable matrix, most notably those published by people from the Eindhoven University of Technology (see Daru & Adams, 1989; Snijder, 1994; Veenendaal, 1994), and those used in the connection with engineering data management. Experimental implementations of the reorderable matrix are reported by Lohringer (1995), Rao & Card (1994) and Schmid & Hinterberger (1994). All these are far too inefficient to be useful in an interactive tool. The purpose of this paper is to discuss the role of the barycenter heuristic in ordering the rows and columns of the matrix. So far, the barycenter heuristic has been mainly used in graph drawing algorithms. In order to gain full advantage of the barycenter heuristic in ordering rows and columns of the reorderable matrix, we survey its use in various contexts and recall the theoretical results obtained.