We introduce an approach to modular dimensionality reduction, allowing efficient learning of multiple complementary representations of the same object. Modules are trained by optimising an unsupervised cost function which balances two competing goals: Maintaining the inner product structure within the original space, and encouraging structural diversity between complementary representations. We derive an efficient learning algorithm which outperforms gradient based approaches without the need to choose a learning rate. We also demonstrate an
intriguing connection with Dropout. Empirical results demonstrate the efficacy of the method for image retrieval and classification.