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In this paper we describe a new nonlinear principal component analyzer and apply it in connection with a new compression scheme to lossy compression of digitized mammograms. We use a 'neural-gas' network for codebook design and several linear and nonlinear principal component method as a preprocessing technique. First, we analyze mathematically the nonlinear, single-layer neural network and show that the equilibrium points of this system are global asymptotically stale. Both a regular Hebbian rule and an anti-Hebbian rule are used for the adaptation of the connection weights between the constituent units. The, we investigate the performance of the compression scheme depending on the blocksize, codebook and number of chosen principal components. The nonlinear principal component method shows the best compression result in combination with the 'neural-gas' network.