The present study presents a new approach to automatic data clustering and classification problems in large and complex databases and, at the same time, derives specific types of explicit rules describing each cluster. The method works well in both sparse and dense multidimensional data spaces. The members of the data space can be of the same nature or represent different classes. A number of N-dimensional ellipsoids are used for enclosing the data clouds. Due to the geometry of an ellipsoid and its free rotation in space the detection of clusters becomes very efficient. The method is based on genetic algorithms that are used for the optimization of location, orientation and geometric characteristics of the hyper-ellipsoids. The proposed approach can serve as a basis for the development of general knowledge systems for discovering hidden knowledge and unexpected patterns and rules in various large databases.