TGMM {TensorClustering}

Fit the Tensor Gaussian Mixture Model (TGMM)

Description

Fit the Tensor Gaussian Mixture Model (TGMM)

Usage

TGMM(Xn, K, shape = "shared", initial = "kmeans", 
iter.max = 500, stop = 1e-3, trueY = NULL, print = FALSE)

Arguments

Xn

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

K

Number of clusters, greater than or equal to 2.

shape

"shared" if assume common covariance across mixtures, "distinct" if allow different covariance structures. Default value is "shared".

initial

Initialization meth0d for the regularized EM algorithm. Default value is "kmeans".

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.

print

Whether to print information including current iteration number, relative change in cluster means and clustering error (%) in each iteration.

Details

The TGMM function fits the Tensor Gaussian Mixture Model (TGMM) through the classical EM algorithm. TGMM assumes the following tensor normal mixture distribution of M-way tensor data \mathbf{X}:

\mathbf{X}\sim\sum_{k=1}^K\pi_k \mathrm{TN}(\bm{\mu}_k,\mathcal{M}_k),\quad i=1,\dots,n,

where 0<\pi_k<1 is the prior probability for \mathbf{X} to be in the k-th cluster such that \sum_{k=1}^{K}\pi_k=1, \bm{\mu}_k is the mean of the k-th cluster, \mathcal{M}_k \equiv \{\bm{\Sigma}_{km}, m=1,\dots,M\} is the set of covariances of the k-th cluster. If \mathcal{M}_k's are the same for k=1,\dots,K, call TGMM with argument shape="shared".

Value

id

A vector of estimated labels.

pi

A vector of estimated prior probabilities for clusters.

eta

A n by K matrix of estimated membership weights.

Mu.est

A list of estimated cluster means.

SIG.est

A list of estimated covariance matrices.

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.

Tait, P. A. and McNicholas, P. D. (2019). Clustering higher order data: Finite mixtures of multidimensional arrays. arXiv:1907.08566.

See Also

TEMM

Examples

  A = array(c(rep(1,20),rep(2,20))+rnorm(40),dim=c(2,2,10))
  myfit = TGMM(A,K=2,shape="shared")