The goal of this work is to develop a technology that can reduce recognition computational complexity with the rise of recognition quality. We use an approach based on implementation of the conjugation indices of the vectors with the class feature spaces. We suggest a new criterion of class separability based on the conjugation index and use it to form so-called support subspaces from the training vectors. This procedure decreases computing complexity at training stage about 1000 times in comparison with previous algorithm implementation and improves recognition quality. The most significant decrease of the computational complexity of the proposed technology is achieved by implementing the fractal compression to radar images. The results prove that using this technology leads to an increase of the recognition quality.