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A novel on-line criterion for identifying "useless" neurons of a self-organizing network is proposed and analyzed. The criterion is based on a utility measure. When it is used in the context of the growing neural gas model to guide deletions of units, the resulting method is able to closely track non-stationary distributions. Slow changes of the distribution are handled by adaptation of existing units. Rapid changes are handled by removal of "useless" neurons and subsequent insertions of new units in other places. Additionally, the utility measure can be used to prune existing networks to a specified size with near-minimal increase of quantization error.