tune_u_joint {TensorClustering}

Tuning envelope dimension jointly by BIC in TEMM.

Description

Tuning envelope dimension jointly by BIC in TEMM.

Usage

tune_u_joint(u_candi, K, X, iter.max = 500, stop = 0.001, trueY = NULL)

Arguments

u_candi

A list of length M containing candidate envelope dimension for each mode.

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.

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

The tune_u_joint function searches over all the combinations of u\equiv(u_1,\dots,u_M) in the neighborhood of \widetilde{u}, \mathcal{N}(\widetilde u)=\{u:\ \max(1,\widetilde u_m-2) \leq u_m \leq \min(\widetilde u_m+2,p_m),\ m=1,\dots,M\}, that minimizes

\mathrm{BIC}(u) = -2\sum_{i=1}^{n}\log(\sum_{k=1}^{K}\widehat{\pi}_k^u f_k(\mathbf{X}_i;\widehat{\bm{\theta}}^u)) + \log(n)\cdot K_u.

In the above BIC, K_u=(K-1)\prod_{m=1}^M u_m + \sum_{m=1}^{M}p_m(p_m+1)/2 is the total number of parameters in TEMM, \widehat{\pi}_k^u and \widehat{\bm{\theta}}^{u} are the estimated parameters with envelope dimension fixed at u. The tune_u_joint function intrinsically selects the initial point and return the optimal estimated labels.

Value

opt.u

Optimal envelope dimension selected.

opt.id

Estimated labels fitted by TEMM with the optimal envelope dimension.

opt.Mu

Estimated cluster means fitted by TEMM with the optimal envelope dimension.

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.

See Also

TEMM, tune_u_sep

Examples

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