Direct domain adaptation through reciprocal linear transformations

We propose a direct domain adaptation (DDA) approach to enrich the training of supervised neural networks on synthetic data by features from real-world data. The process involves a series of linear operations on the input features to the NN model, whether they are from the source or target distributions, as follows: (1) A cross-correlation of the input data (i.e., images) with a randomly picked sample pixel (or pixels) of all images from the input or the mean of all randomly picked sample pixel (or pixels) of all input images. (2) The convolution of the resulting data with the mean of the autocorrelated input images from the other domain. In the training stage, as expected, the input images are from the source distribution, and the mean of auto-correlated images are evaluated from the target distribution. In the inference/application stage, the input images are from the target distribution, and the mean of auto-correlated images are evaluated from the source distribution. The proposed method only manipulates the data from the source and target domains and does not explicitly interfere with the training workflow and network architecture. An application that includes training a convolutional neural network on the MNIST dataset and testing the network on the MNIST-M dataset achieves a 70% accuracy on the test data. A principal component analysis (PCA), as well as t-SNE, shows that the input features from the source and target domains, after the proposed direct transformations, share similar properties along the principal components as compared to the original MNIST and MNIST-M input features.