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The clustering algorithms based on deep neural network perform clustering by obtaining the optimal feature representation. However, in the face of complex natural images, the cluster accuracy of existing clustering algorithms is still relatively low. This paper presents an image clustering algorithm based on predefined evenly-distributed class centroids (PEDCC) and composite cosine distance. Compared with the current popular auto-encoder structure, we design an encoder-only network structure with normalized latent features, and two effective loss functions in latent feature space by replacing the Euclidean distance with a composite cosine distance. We find that (1) contrastive learning plays a key role in the clustering algorithm and greatly improves the quality of learning latent features; (2) compared with the Euclidean distance, the composite cosine distance can be more suitable for the normalized latent features and PEDCC-based Maximum Mean Discrepancy (MMD) loss function; and (3) for complex natural images, a self-supervised pretrained model can be used to effectively improve clustering performance. Several experiments have been carried out on six common data sets, MNIST, Fashion-MNIST, COIL20, CIFAR-10, STL-10 and ImageNet-10. Experimental results show that our method achieves the best clustering effect compared with other latest clustering algorithms.