tune_K: Select the number of clusters 'K' in DEEM

In azuryee/TensorClustering: Model-Based Tensor Clustering

Description

Select the number of clusters K along with tuning parameter lambda through BIC in DEEM.

Usage

tune_K(X, seqK, seqlamb, initial = TRUE, vec_x = NULL)

Arguments

X	Input tensor (or matrix) list of length n, where n is the number of observations. Each element of the list is a tensor or matrix. The order of tensor can be any positive integer not less than 2.
seqK	A sequence of user-specified number of clusters.
seqlamb	A sequence of user-specified lambda values. lambda is the weight of L1 penalty and a smaller lambda allows more variables to be nonzero
initial	Whether to initialize algorithm with K-means clustering. Default value is TRUE.
vec_x	Vectorized tensor data. Default value is NULL

Details

The tune_K function runs tune_lamb function length(seqK) times to choose the tuning parameter λ and number of clusters K simultaneously. Let \widehat{\bm{θ}}^{\{λ,K\}} be the output of DEEM with the tuning parameter and number of clusters fixed at λ and K respectively, tune_K looks for the values of λ and K that minimizes

\mathrm{BIC}(λ,K)=-2∑_{i=1}^n\log(∑_{k=1}^K\widehat{π}^{\{λ,K\}}_kf_k(\mathbf{X}_i;\widehat{\bm{θ}}_k^{\{λ,K\}}))+\log(n)\cdot |\widehat{\mathcal{D}}^{\{λ,K\}}|,

where \widehat{\mathcal{D}}^{\{λ,K\}}=\{(k, {\mathcal{J}}): \widehat b_{k,{\mathcal{J}}}^{λ} \neq 0 \} is the set of nonzero elements in \widehat{\bm{B}}_2^{\{λ,K\}},…,\widehat{\bm{B}}_K^{\{λ,K\}}. The tune_K function intrinsically selects the initial point and return the optimal estimated labels.

Value

opt_K	Selected number of clusters that leads to optimal BIC.
opt_lamb	Tuned lambda that leads to optimal BIC.
Krank	A selection summary.

Author(s)

Kai Deng, Yuqing Pan, Xin Zhang and Qing Mai

References

Mai, Q., Zhang, X., Pan, Y. and Deng, K. (2021). A Doubly-Enhanced EM Algorithm for Model-Based Tensor Clustering. Journal of the American Statistical Association.

See Also

DEEM, tune_lamb

Examples

dimen = c(5,5,5)
nvars = prod(dimen)
K = 2
n = 100
sigma = array(list(),3)

sigma[[1]] = sigma[[2]] = sigma[[3]] = diag(5)

B2=array(0,dim=dimen)
B2[1:3,1,1]=2

y = c(rep(1,50),rep(2,50))
M = array(list(),K)
M[[1]] = array(0,dim=dimen)
M[[2]] = B2

vec_x=matrix(rnorm(n*prod(dimen)),ncol=n)
X=array(list(),n)
for (i in 1:n){
  X[[i]] = array(vec_x[,i],dim=dimen)
  X[[i]] = M[[y[i]]] + X[[i]]
}

mytune = tune_K(X, seqK=2:4, seqlamb=seq(0.01,0.1,by=0.01))

azuryee/TensorClustering documentation built on June 28, 2021, 8:06 p.m.