In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolutional kernel networks (CKNs) in the context of unsupervised learning; then, we derive backpropagation rules to take advantage of labeled training data. The resulting model is a new type of convolutional neural network, where optimizing the filters at each layer is equivalent to learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We show that our method achieves reasonably competitive performance for image classification on some standard ``deep learning'' datasets such as CIFAR-10 and SVHN, and also for image super-resolution, demonstrating the applicability of our approach to a large variety of image-related tasks.

This paper proposes an original idea and theoretically appealing solutions to solve it. Quality: Its first part (Section 1, 2) is excellent, but its latter part may be a little weak. Section 3 is a little dense with numerous details and heuristics. A pseudo-code showing the overall framework may be helpful for readers. Section 4 is a little short to validate the potential effectiveness of the proposed method. A direct comparison between CKN and CNN with same architecture may be more informative for readers.