  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 domains, 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 that domain or the mean of
all randomly picked sample pixel (or pixels) of all 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 domain, and the mean of auto-correlated images are evaluated from the
target domain. In the inference/application stage, the input images are from
the target domain, and the mean of auto-correlated images are evaluated from
the source domain. 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, show that the input features from
the source and target domains, after the proposed direct transformations, share
similar properties along with the principal components as compared to the
original MNIST and MNIST-M input features.
