Optimal Clustering with Missing Values

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Missing values frequently arise in modern biomedical studies due to various reasons, including missing tests or complex profiling technologies for different omics measurements. Missing values can complicate the application of clustering algorithms, whose goals are to group points based on some similarity criterion. A common practice for dealing with missing values in the context of clustering is to first impute the missing values, and then apply the clustering algorithm on the completed data. The performance of such methods, however, depends on the knowledge of missing value mechanism, which is rarely fully achievable in practice. We consider missing values in the context of optimal clustering, which finds an optimal clustering operator with reference to an underlying random labeled point process (RLPP). We present how the missing-value problem fits neatly into the overall framework of optimal clustering by marginalizing out the missing-value process from the feature distribution. In particular, we demonstrate the proposed framework for the multivariate Gaussian model with an arbitrary covariance structure. Comprehensive experimental studies on both synthetic and real-world RNA-seq data shows the superior performance of the proposed optimal clustering with missing values, compared to various clustering approaches, including k-means, fuzzy c-means and hierarchical clustering, with the off-the-shelf Gibbs sampling based imputation method. Optimal clustering offers a robust and flexible framework for dealing with the missing value problem, obviating the need for imputation-based pre-processing of the data. Its superior performance compared to various clustering methods in settings with different missing rates and small sample sizes, demonstrates the optimal clusterer as a promising tool for dealing with missing data in biomedical applications.