Compressed learning (CL) is a joint signal processing and machine learning framework for inference from a signal, using a small number of measurements obtained by a linear projection. In this chapter, we review this concept of compressed leaning, which suggests that learning directly in the compressed domain is possible, and with good performance. We experimentally show that the classification accuracy, using an efficient classifier in the compressed domain, can be quite close to the accuracy obtained when operating directly on the original data. Using convolutional neural network for the image classification, we examine the performance of different linear sensing schemes for the data acquisition stage, such as random sensing and PCA projection. Then, we present an end-to-end deep learning approach for CL, in which a network composed of fully connected layers followed by convolutional ones, performs the linear sensing and the nonlinear inference stages simultaneously. During the training phase, both the sensing matrix and the nonlinear inference operator are jointly optimized, leading to a suitable sensing matrix and better performance for the overall task of image classification in the compressed domain. The performance of the proposed approach is demonstrated using the MNIST and CIFAR-10 datasets.

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