Concentration of Entries in Binary Arrays

NUMERICAL methods for the classification of elements into sets commonly begin with an assortment of individuals defined by the possession or non-possession of a number of attributes, and seek to provide final sets of highly similar individuals1,2. The attribute-groups which form the basis of such a classification may also be of interest, in which case the system may be transposed and the attributes classified into groups by reference to the individuals3. Finally, attempts have been made4 to extract ‘noda’, simultaneously defined by a final set of individuals and by a final set of attributes. Existing methods for the extraction of such noda sub-divide individuals and attributes independently and collate the results by reference to a ‘two-way table’; but such methods do not provide the most efficient concentration of positive entries. It should in principle be possible to obtain each block substantially independently of the others, concentrating its entries by reference to such individuals and attributes as are involved in it; but, except in the trivial case of the ‘black-and-white’ table, it is not to be expected that the blocks will then dispose themselves conveniently within the cells of a conventional two-wray table. Some may be expected to do so, but some will almost certainly transgress cell-boundaries and/or occupy only part of the fixed cells.