Likelihood linkage analysis (LLA) classification method: an example treated by hand.

This paper describes a very general method of data analysis using a hierarchical classification. The data can be provided by observation, experiment or knowledge; their nature can be numerical, qualitative or logical. First, the classical view of the context of data representation, in which the algorithm of hierarchical ascendant construction of the classification tree is set, is treated in a synthetic manner. The main notion in our method is one of 'similarity'. This must be elaborated in the best way, taking into account the mathematical nature of the objects to be compared. Here we adopt a set of theoretical and combinatorial representation of the descriptive attributes, which are interpreted in terms of relations. Then we introduce a probability scale for similarity measurement by using a likelihood concept. The largest part of the paper concerns an illustrating example, moderately sized, detailing very minutely the different steps and the different calculations assumed by the method. The data structure handled with this example is the simplest possible. Then, general aspects and methodological extensions are evoked. We end by indicating the interest of the described approach in future works, in which we are involved, concerning typological organization of genetic sequences. We emphasize the 'explanation' aspect of the obtained results, with respect to a given description. For this purpose, classifications (on the object set and on the attribute set) on the one hand and machine learning techniques on the other, intervene efficiently.

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