A Generalisation of the Mixture Decomposition Problem in the Symbolic Data Analysis Framework
Diday, Edwin (2001), A Generalisation of the Mixture Decomposition Problem in the Symbolic Data Analysis Framework. https://basepub.dauphine.fr/handle/123456789/6619
TypeDocument de travail / Working paper
Series titleCahiers du CEREMADE
MetadataShow full item record
Abstract (EN)In Symbolic Data Analysis, more complex units can be considered like "concepts" (as towns, insurance companies, species of animals). A concept can be characterized by an "extent" defined by a class of standard units called "individuals" (as a sample of inhabitant of a town, a sample of insurance companies, a sample of animals of a given species). These classes can be described by a distribution associated to each variable, summarizing in that way huge sets of data. Therefore, here we are interested by the case where each unit representing a "concept" is described by a vector of p distributions associated to p variables. Our aim is to find simultaneously a "good" partition of these units and a model using "copulas" associated to each class of this partition. Different copulas models are recalled where the case of Markov process and Brownian motion are considered. The mixture decomposition problem is settled in this general case. It extends the standard mixture decomposition problem to the case where each unit is described by a vector of distributions instead as usual, by a vector of unique (categorical or numerical) values. Several generalization of standard algorithms are suggested. One of them is illustrated by a simple example. All these results are first considered in the case of a unique variable and then extended to the case of a vector of p variables by using a top-down binary tree approach. Finally, the case of infinite joint and copulas is considered.
Subjects / KeywordsPartitioning; Clustering; Data Mining; Symbolic Data Analysis; Mixture decomposition
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