A Short Note on Empirical Penalty Term Study of BIC in K-means Clustering Inverse Regression

According to recent studies, Bayesian information criteria(BIC) is proposed to determine the structural dimension of the central subspace through sliced inverse regression(SIR) with high-dimensional predictors. The BIC may be useful in K-means clustering inverse regression(KIR) with high-dimensional predictors. However, the direct application of the BIC to KIR may be problematic, because the slicing scheme in SIR is not the same as that of KIR. In this paper, we present empirical penalty term studies of BIC in KIR to identify the most appropriate one. Numerical studies and real data analysis are presented.