Expert Constrained Clustering: A Symbolic Approach
A new constrained model is discussed as a way of incorporating efficiently a priori expert knowledge into a clustering problem of a given individual set. The first innovation is the combination of fusion constraints, which request some individuals to belong to one cluster, with exclusion constraints, which separate some individuals in different clusters. This situation implies to check the existence of a solution (ie if no pair of individuals are connected by fusion and exclusion constraints). The second novelty is that the constraints are expressed in a symbolic language that allows compact description of group of individuals according to a given interpretation. This paper studies the coherence of such constraints at individual and symbolic levels. A mathematical framework, close to the Symbolic Data Analysis, is built in order to define how a symbolic description space may be interpreted on a given individual set. A partial order on symbolic descriptions (which is an usual assumption of Artificial Intelligence), allows a symbolic analysis of the constraints. Our results provide an individual but also a symbolic clustering.
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