In this paper we propose a novel and robust optimization scheme allowing to obtain the Karhunen-Lo`eve transform up to the permutation of row vectors. The introduced scheme is designed to be used in connection with artificial neural networks trained with the aid of gradient optimization techniques, and it involves two optimization criteria: (i) minimization of the mean squared error of signal reconstruction, (ii) minimization of the entropy related criterion. It should be noted that the proposed scheme implies possibly minimal constraints, which are commonly used in the tasks of training of artificial neural networks, and hence, it can be easily applied to the practical applications using popular and widely available software and hardware tools. The effectiveness of the proposed scheme is verified experimentally using model signals.