We propose a novel self-organizing neural network for the unsupervised classification of electron microscopy (EM) images of biological macromolecules. The radical novelty of the algorithm lies in its rigorous mathematical formulation that, starting from a large set of possibly very noisy input data, finds a set of "representative" data items, organized onto an ordered output map, such that the probability density of this set of representative items resembles at its possible best the probability density of the input data. In a way, it summarizes large amounts of information into a concise description that rigorously keeps the basic pattern of the input data distribution. In this application to the field of three-dimensional EM of single particles, two different data sets have been used; one comprised 2458 rotational power spectra of individual negative stain im-ages of the G40P helicase of Bacillus subtilis bacteriophage SPP1, and the other contained 2822 cryoelectron images of SV40 large T-antigen. Our experimental results prove that this technique is indeed very successful, providing the user with the capability of exploring complex patterns in a succinct, informative, and objective manner. The above facts, together with the consideration that the integration of this new algorithm with commonly used software packages is immediate, prompt us to propose it as a valuable new tool in the analysis of large collections of noisy data.