Abstract
The classification problem where each object is given by a set of multidimensional measurements that is associated with an unknown dependence is considered. Intersection of sets that define objects from different classes is allowed. In this case, it is natural to found classification algorithms based on the difference between dependencies for the objects belonging to different classes. Two algorithms to convert the set classification problem solution from the initial feature space into (1) the parameters space of the common model structure for all the objects and (2) the parameters spaces of the best structures for each class are proposed, along with a classification algorithm based on the accuracy of object representation by the models based on the structures found for each class. If the objects are described with big data, the approach can be used to transform data into a compact form (model parameters) that preserves the characteristics that are necessary to separate the classes. An approach to solve a problem of clustering sets is proposed. Some examples are given.
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