  Flow cytometry is a technology that rapidly measures antigen-based markers
associated to cells in a cell population. Although analysis of flow cytometry
data has traditionally considered one or two markers at a time, there has been
increasing interest in multidimensional analysis. However, flow cytometers are
limited in the number of markers they can jointly observe, which is typically a
fraction of the number of markers of interest. For this reason, practitioners
often perform multiple assays based on different, overlapping combinations of
markers. In this paper, we address the challenge of imputing the high
dimensional jointly distributed values of marker attributes based on
overlapping marginal observations. We show that simple nearest neighbor based
imputation can lead to spurious subpopulations in the imputed data, and
introduce an alternative approach based on nearest neighbor imputation
restricted to a cell's subpopulation. This requires us to perform clustering
with missing data, which we address with a mixture model approach and novel EM
algorithm. Since mixture model fitting may be ill-posed, we also develop
techniques to initialize the EM algorithm using domain knowledge. We
demonstrate our approach on real flow cytometry data.

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