Profiles are proportions that are calculated from the counts, nij, in the original contingency table. Specifically, the profile for row i is (ni1 / ni., ..., nic / ni.); the profile for column j is (n1j / n.j, ..., nrj / n.j).
The average row profile is calculated from the column totals. Specifically, the average row profile is (n.1 / n, ..., n.c / n). Similarly, the average column profile is calculated from the row totals. Specifically, the average column profile is (n1. / n,..., nr. / n).