an unsupervised back propagation method for training neural networks . for a set of inputs , target outputs are assigned l &# 39 ; s and o &# 39 ; s randomly or arbitrarily for a small number of outputs . the learning process is initiated and the convergence of outputs towards targets is monitored . at intervals , the learning is paused , and the values for those targets for the outputs which are converging at a less than average rate , are changed , and the learning is then resumed with the new targets . the process is continuously iterated and the outputs converge on a stable classification , thereby providing unsupervised back propagation . in a further embodiment , samples classified with the trained network may serve as the training sets for additional subdivisions to grow additional layers of a hierarchical classification tree which converges to indivisible branch tips . after training is completed , such a tree may be used to classify new unlabelled samples with high efficiency . in yet another embodiment , the unsupervised back propagation method of the present invention may be adapted to classify fuzzy sets .