Currently most of image classification tasks are achieved by supervised learning. High-quality datasets naturally bring difficulties in annotation, and the datasets in real-world applications present a nonlinear structure, and the annotation cost grows exponentially with the number of targets and the difficulty of recognisability. In this context, research about unsupervised image classification is the way to go. Traditional unsupervised learning for classification is mostly based on the Euclidean distance and various paradigms, which is unable to extract the nonlinear structure of the dataset. This shortcoming makes the accuracy of traditional unsupervised image classification drop drastically. In this paper, we propose to first extract the nonlinear structure of the original dataset using the manifold learning method, and then produce pseudo-labels through the agglomerative clustering algorithm. The pseudo-labels obtained in this way can effectively retain the special mathematical structure of the original data with high accuracy. The neural network is trained with these pseudo labels to obtain an unsupervised usable image classifier. The classifier can be trained on small-scale data and then applied to large-scale data sets, thus saving the cost of manual labelling. The experiments are carried out by setting up a control group and two manifold learning groups for the extraction of non-linear structures using LLE and Isomap algorithms respectively. After that, the production of pseudo-labels and the training of neural networks are completed, and the accuracy of the three groups is compared. Finally, it is concluded that the correct rate of the two groups that have gone through the manifold learning algorithm to extract the nonlinear structure is much higher than that of the other one, and the image classifier based on the Isomap algorithm achieves an accuracy of 85% in the test set, which is highly practical.