Abstract: Convolutional neural network （CNN） has achieved great success in semi-supervised learning. It uses both labelled samples and unlabelled samples in the training stage. Unlabelled samples can help standardize the learning model. To further improve the feature extraction ability of semi-supervised models， this paper proposes an end-to-end semi-supervised learning method combining deep semi-supervised convolutional neural network and sparse coding dictionary learning， called Semi-supervised Learning based on Sparse Coding and Convolution （SSSConv）， which aims to learn more discriminative image feature representation and improve the performance of classification tasks. Firstly， the proposed method uses CNN to extract features and performs orthogonal projection transformation on them. Then， learn the corresponding sparse coding and obtain the image representation. Finally， the classifier of the model can classify them. The whole semi-supervised learning process can be regarded as an end-to-end optimization problem. CNN part and sparse coding part have a unified loss function. In this paper， conjugate gradient descent algorithm， chain rule， and backpropagation algorithm are used to optimize the parameters of the objective function. Among them， we restrict the relevant parameters of sparse coding to the manifold， and the CNN parameters can be defined not only in Euclidean space but also in orthogonal space. Experimental results based on semi-supervised classification tasks verify the effectiveness of the proposed SSSConv framework， which is highly competitive with existing methods.

Key words: sparse representation, dictionary learning, convolutional neural network, semi-supervised learning, manifold, geometric optimization