Gaussian mixture model (GMM) clustering has been extensively studied due to its effectiveness and efficiency. Though demonstrating promising performance in various applications, it cannot effectively address the absent features among data, which is not uncommon in practical applications. In this article, different from existing approaches that first impute the absence and then perform GMM clustering tasks on the imputed data, we propose to integrate the imputation and GMM clustering into a unified learning procedure. Specifically, the missing data is filled by the result of GMM clustering, and the imputed data is then taken for GMM clustering. These two steps alternatively negotiate with each other to achieve optimum. By this way, the imputed data can best serve for GMM clustering. A two-step alternative algorithm with proved convergence is carefully designed to solve the resultant optimization problem. Extensive experiments have been conducted on eight UCI benchmark datasets, and the results have validated the effectiveness of the proposed algorithm.

中文翻译：

---

不完整数据的高斯混合模型聚类

高斯混合模型（GMM）聚类因其有效性和效率而被广泛研究。尽管在各种应用中表现出良好的性能，但它不能有效地解决数据中缺失的特征，这在实际应用中并不少见。在本文中，与现有的先估算缺失然后对估算数据执行 GMM 聚类任务的方法不同，我们建议将估算和 GMM 聚类集成到一个统一的学习过程中。具体而言，缺失数据由 GMM 聚类的结果填充，然后将插补数据用于 GMM 聚类。这两个步骤交替地相互协商以达到最佳效果。通过这种方式，估算的数据可以最好地服务于 GMM 聚类。精心设计了具有证明收敛性的两步替代算法来解决由此产生的优化问题。对八个 UCI 基准数据集进行了广泛的实验，结果验证了所提出算法的有效性。