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Getting deep convolutional neural networks to perform well requires a large amount of training data. When the available labelled data is small, it is often beneficial to use transfer learning to leverage a related larger dataset (source) in order to improve the performance on the small dataset (target). Among the transfer learning approaches, domain adaptation methods assume that distributions between the two domains are shifted and attempt to realign them. In this paper, we consider the domain adaptation problem from the perspective of dimensionality reduction and propose a generic framework based on graph embedding. Instead of solving the generalised eigenvalue problem, we formulate the graph-preserving criterion as a loss in the neural network and learn a domain-invariant feature transformation in an end-to-end fashion. We show that the proposed approach leads to a powerful Domain Adaptation framework; a simple LDA-inspired instantiation of the framework leads to state-of-the-art performance on two of the most widely used Domain Adaptation benchmarks, Office31 and MNIST to USPS datasets.