Analogical Dissimilarity: Definition, Algorithms and Two Experiments in Machine Learning

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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.