  In this paper, we consider feature screening for ultrahigh dimensional
clustering analyses. Based on the observation that the marginal distribution of
any given feature is a mixture of its conditional distributions in different
clusters, we propose to screen clustering features by independently evaluating
the homogeneity of each feature's mixture distribution. Important
cluster-relevant features have heterogeneous components in their mixture
distributions and unimportant features have homogeneous components. The
well-known EM-test statistic is used to evaluate the homogeneity. Under general
parametric settings, we establish the tail probability bounds of the EM-test
statistic for the homogeneous and heterogeneous features, and further show that
the proposed screening procedure can achieve the sure independent screening and
even the consistency in selection properties. Limiting distribution of the
EM-test statistic is also obtained for general parametric distributions. The
proposed method is computationally efficient, can accurately screen for
important cluster-relevant features and help to significantly improve
clustering, as demonstrated in our extensive simulation and real data analyses.
