Visualization of clusters in very large rectangular dissimilarity data

D is an m×n matrix of pairwise dissimilarities between m row objects Or and n column objects Oc, which, taken together, comprise m+n objects O = [o <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> ,…o <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> ,o <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m+1</inf> ,…o <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m+n</inf> ]. There are four clustering problems associated with O: (P1) amongst the row objects O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> ; (P2) amongst the column objects O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> ; (P3) amongst the union of the row and column objects O=O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> ∪O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> ; and (P4) amongst the union of the row and column objects that contain at least one object of each type (co-clusters). The coVAT algorithm, which builds images for visual assessment of clustering tendency for these problems, is limited to m×n ≈ O(10 4 ×10 4 ). We develop a scalable version of coVAT that approximates coVAT images when D is very large. Two examples are given to illustrate and evaluate the new method.