tune_u_sep {TensorClustering}

Tuning envelope dimension separately by BIC in TEMM.

Description

Tuning envelope dimension separately by BIC in TEMM.

Usage

tune_u_sep(m, u_candi, K, X, C = 1, oneD = TRUE, 
iter.max = 500, stop = 0.001, trueY = NULL)

Arguments

m

The tensor mode to be tuned, can take value in 1,...,M.

u_candi

A vector of candidate envelope dimension.

K

Number of clusters, greater than or equal to 2.

X

The tensor for clustering, should be array type, the last dimension is the sample size n.

C

Constant in separate BIC criterion. Default value is 1.

oneD

Whether to apply 1D-BIC tuning. Default value is TRUE.

iter.max

Maximum number of iterations. Default value is 500.

stop

Convergence threshold of relative change in cluster means. Default value is 1e-3.

trueY

A vector of true cluster labels of each observation. Default value is NULL.

Details

For tensor mode m=1,\dots,M, the tune_u_sep function selects the envelope dimension \widetilde{u}_m by minimizing the following BIC-type criterion over the set \{0,1,\dots,p_m\},

\mathrm{BIC}_m(u_m) = \log|\bm{\Gamma}_m^T \widehat{\mathbf{M}}_m \bm{\Gamma}_m|+\log|\bm{\Gamma}_{m}^T \widehat{\mathbf{N}}_m^{-1} \bm{\Gamma}_{m}| + C \cdot u_m \log(n)/n.

This separate selection over each mode m is less sensitive to the complex interrelationships of each mode of the tensor. The default constant C is set as 1 as suggested by Zhang and Mai (2018).

Value

opt.u

Optimal envelope dimension selected.

bic

BIC value.

Author(s)

Kai Deng, Yuqing Pan, Xin Zhang and Qing Mai

References

Deng, K. and Zhang, X. (2021). Tensor Envelope Mixture Model for Simultaneous Clustering and Multiway Dimension Reduction. Biometrics.

Zhang, X. and Mai, Q. (2018). Model-free envelope dimension selection. Electronic Journal of Statistics 12, 2193-2216.

See Also

TEMM, tune_u_joint

Examples

  A = array(c(rep(1,20),rep(2,20))+rnorm(40),dim=c(2,2,10))
  mytune = tune_u_sep(1,1:2,K=2,A)