  This paper defines the notion of analogical dissimilarity between four
objects, with a special focus on objects structured as sequences. Firstly, it
studies the case where the four objects have a null analogical dissimilarity,
i.e. are in analogical proportion. Secondly, when one of these objects is
unknown, it gives algorithms to compute it. Thirdly, it tackles the problem of
defining analogical dissimilarity, which is a measure of how far four objects
are from being in analogical proportion. In particular, when objects are
sequences, it gives a definition and an algorithm based on an optimal alignment
of the four sequences. It gives also learning algorithms, i.e. methods to find
the triple of objects in a learning sample which has the least analogical
dissimilarity with a given object. Two practical experiments are described: the
first is a classification problem on benchmarks of binary and nominal data, the
second shows how the generation of sequences by solving analogical equations
enables a handwritten character recognition system to rapidly be adapted to a
new writer.
