For data clustering, Gaussian mixture model (GMM) is a typical method that trains several Gaussian models to capture the data. Each Gaussian model then provides the distribution information of a cluster. For clustering of high dimensional and complex data, more flexible models rather than Gaussian models are desired. Recently, the generative adversarial networks (GANs) have shown effectiveness in capturing complex data distribution. Therefore, GAN mixture model (GANMM) would be a promising alternative of GMM. However, we notice that the non-flexibility of the Gaussian model is essential in the expectation-maximization procedure for training GMM. GAN can have much higher flexibility, which disables the commonly employed expectation-maximization procedure, as that the maximization cannot change the result of the expectation. In this paper, we propose to use the epsilon-expectation-maximization procedure for training GANMM. The experiments show that the proposed GANMM can have good performance on complex data as well as simple data.

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In multi-label classification tasks, labels are commonly related with each other. It has been well recognized that utilizing label relationship is essential to multi-label learning. One way to utilizing label relationship is to map labels to a lower-dimensional space of uncorrelated labels, where the relationship could be encoded in the mapping. Previous linear mapping methods commonly result in regression subproblems in the lower-dimensional label space. In this paper, we disclose that mappings to a low-dimensional multi-label regression problem can be worse than mapping to a classification problem, since regression requires more complex model than classification. We then propose the binary linear compression (BILC) method that results in a binary label space, leading to classification subproblems. Experiments on several multi-label datasets show that, employing classification in the embedded space results in much simpler models than regression, leading to smaller structure risk. The proposed methods are also shown to be superior to some state-of-the-art approaches.