  Most of existing clustering algorithms are proposed without considering the
selection bias in data. In many real applications, however, one cannot
guarantee the data is unbiased. Selection bias might bring the unexpected
correlation between features and ignoring those unexpected correlations will
hurt the performance of clustering algorithms. Therefore, how to remove those
unexpected correlations induced by selection bias is extremely important yet
largely unexplored for clustering. In this paper, we propose a novel
Decorrelation regularized K-Means algorithm (DCKM) for clustering with data
selection bias. Specifically, the decorrelation regularizer aims to learn the
global sample weights which are capable of balancing the sample distribution,
so as to remove unexpected correlations among features. Meanwhile, the learned
weights are combined with k-means, which makes the reweighted k-means cluster
on the inherent data distribution without unexpected correlation influence.
Moreover, we derive the updating rules to effectively infer the parameters in
DCKM. Extensive experiments results on real world datasets well demonstrate
that our DCKM algorithm achieves significant performance gains, indicating the
necessity of removing unexpected feature correlations induced by selection bias
when clustering.
