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Clustering is a challenging and crucial task in unsupervised learning. Recently, though many clustering algorithms combined with deep learning have been proposed, we observe that the existing deep clustering algorithms do not considerably preserve the clustering structure and information of raw data in the learned latent space. To address this issue, we propose a Generative Adversarial Attention Clustering network Based on Inverse autoencoder (IAE-ClusterGAN), which can control the distribution type of the learned latent code without additional constraints so that unsupervised clustering tasks can be done efficiently. Meanwhile, we integrate the attention mechanism into the network to make the latent code contain more useful clustering information. Moreover, we utilize hyperspherical mapping in the discriminator to improve the stability of model training and reduce the training parameters. Experimental results demonstrate that IAE-ClusterGAN achieves competitive results compared to the state-of-the-art models on five benchmark datasets.