Unsupervised learning of Dirichlet process mixture models with missing data

This study presents a novel approach to unsupervised learning for clustering with missing data. We first extend a finite mixture model to the infinite case by considering Dirichlet process mixtures, which can automatically determine the number of mixture components or clusters. Furthermore, we view the missing features as latent variables and compute the posterior distributions using the variational Bayesian expectation maximization algorithm, which optimizes the evidence lower bound on the complete-data log marginal likelihood. We demonstrate the performance on several artificial data sets with missing values. The experimental results indicate that the proposed method outperforms some classic imputation methods. We finally present an application to seabed hydrothermal sulfide color images analysis problem.创新点本文提出了一种能够用于处理缺失数据的无监督聚类学习方法。首先,我们将Dirichlet过程作为先验分布引入到有限混合模型中,实现聚类数目或混合成分数的自动识别。其次,针对观测样本不同维度数据存在缺失的问题,我们将缺失成分当成隐变量参数,利用变分贝叶斯期望最大化算法优化完全观测数据边际似然函数的下界,对参数的后验分布进行求解。通过和几种典型的插补方法进行对比实验,验证了本文所提出方法的有效性。最后,将该方法应用于深海热液硫化物图像分析,完成图像的自动分类任务。