tune_u_joint: Tuning envelope dimension jointly by BIC in TEMM.
In azuryee/TensorClustering: Model-Based Tensor Clustering

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/tune_u_joint.R

Tuning envelope dimension jointly by BIC in TEMM.

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

`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.

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

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

In the above BIC, K_u=(K-1)∏_{m=1}^M u_m + ∑_{m=1}^{M}p_m(p_m+1)/2 is the total number of parameters in TEMM, \widehat{π}_k^u and \widehat{\bm{θ}}^{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.

`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.