We will present the notion of analogical proportion and of analogical dissimilarity between four objects, with a special focus on objects structured as sequences.The analogical dissimilarity is a measure of how far four objects are from being in analogical proportion. In particular, when objects are sequences, we give a definition and an algorithm based on an optimal alignment of the four sequences. We will also show how to use this concept in machine learning. Two practical experiments will be 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.

Reference article :
Laurent Miclet, Sabri Bayoudh, and Arnaud Delhay.
Analogical dissimilarity : De?nition, algorithms and two experiments in machine learning.
Journal of Arti?ciel Intelligence Research, 32, August 2008.