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Convolutional neural networks are known to be powerful image classifiers. In this work, a method is proposed for training convolutional networks for implementation on an existing mixed digital-analog VLSI hardware architecture. The binary threshold neurons provided by this architecture cannot be trained using gradient-based methods. The convolutional layers are trained with a clustering method, locally in each layer. The output layer is trained using the Perceptron learning rule. Competitive results are obtained on hand-written digits (MNIST) and traffic signs. The analog hardware enables high integration and low power consumption, but inherent error sources affect the computation accuracy. Networks trained as suggested are highly robust against random changes of synaptic weights occuring on the hardware substrate, and work well even with only three distinct weight values (-1, 0, +1), reducing computational complexity to mere counting.