What it has been previously developed visually, now it can be found automatically by choosing in each vertex of the lattice of the topology T(E1), the line that conducts to the vertex of the lattice of the topology T(E2) with a larger number of elements, that is, attributes. From another perspective, if we consider all the elements of the topology T(E1), that is, titles and groups of titles, and the subsets of attributes possessed by all of them are found visually in the matrix. If a topology T(E1) has a lower number of elements than other topology T(E2), the correspondence of each element of T(E1) goes to only one element of T(E2). This is interesting in order to develop an algorithm for groupings. At least, there exists a correspondence between both topologies. In the business and in the economic environment, it becomes interesting to analyze this type of correspondence, especially when we want to establish homogeneous groupings or segmentation processes. The same result is found by using one of the algorithms used for obtaining affinities (Kaufmann and Gil-Aluja, 1991). But then, it is necessary to consider, in the relation between the set of titles and the set of attributes, all the elements of the power set of both sets. Then, starting from the same matrix and using the algorithm of the maximum inverse correspondence (Gil-Aluja, 1999) we find the right connection. By choosing for all the elements of the power set E2 the element of the power set of E1 with the largest number of components. As we can see, the result is the same as the one found with the new algorithm. Sometimes, the topologies T(E1) and T(E2) are the same than the power set of both sets E1 and E2, as it happens in the following problem (Gil-Aluja and Gil-Lafuente, 2007). Note that this result is the same than the result that appears in the work (Gil-Aluja and Gil-Lafuente, 2007) that uses an assignment algorithm.