  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.
  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 show how the missing-value problem fits neatly into
the overall framework of optimal clustering by incorporating the missing value
mechanism into the random labeled point process and then marginalizing out the
missing-value process. In particular, we demonstrate the proposed framework for
the Gaussian model with arbitrary covariance structures. Comprehensive
experimental studies on both synthetic and real-world RNA-seq data show the
superior performance of the proposed optimal clustering with missing values
when compared to various clustering approaches. Optimal clustering with missing
values obviates the need for imputation-based pre-processing of the data, while
at the same time possessing smaller clustering errors.
