Optimal unions of hidden classes

The cluster analysis is a traditional tool for multi-varietal data processing. Using the k-means method, we can split a pattern set into a given number of clusters. These clusters can be used for the final classification of known output classes. This paper focuses on various approaches that can be used for an optimal union of hidden classes. The resulting tasks include binary programming or convex optimization ones. Another possibility of obtaining hidden classes is designing imperfect classifier system. Novel context out learning approach is also discussed as possibility of using simple classifiers as background of the system of hidden classes which are easy to union to output classes using the optimal algorithm. All these approaches are useful in many applications, including econometric research. There are two main methodologies: supervised and unsupervised learning based on given pattern set with known or unknown output classification. Preferring supervised learning, we can combine the context out learning with optimal union of hidden classes to obtain the final classifier. But if we prefer unsupervised learning, we will begin with cluster analysis or another similar approach to also obtain the hidden class system for future optimal unioning. Therefore, the optimal union algorithm is widely applicable for any kind of classification tasks. The presented techniques are demonstrated on an artificial pattern set and on real data related to crisis prediction based on the clustering of macroeconomic indicators.