MGRAF2 {CISE} R Documentation

## Second variant of M-GRAF model

### Description

`MGRAF2` returns the estimated common structure Z and Λ that are shared by all the subjects as well as the subject-specific low rank matrix Q_i for multiple undirected graphs.

### Usage

```MGRAF2(A, K, tol, maxit)
```

### Arguments

 `A` Binary array with size VxVxn storing the VxV symmetric adjacency matrices of n graphs. `K` An integer that specifies the latent dimension of the graphs `tol` A numeric scalar that specifies the convergence threshold of CISE algorithm. CISE iteration continues until the absolute percent change in joint log-likelihood is smaller than this value. Default is tol = 0.01. `maxit` An integer that specifies the maximum number of iterations. Default is maxit = 5.

### Details

The subject-specific deviation D_i is decomposed into

D_i = Q_i * Λ * Q_i^{\top},

where each Q_i is a VxK orthonormal matrix and Λ is a KxK diagonal matrix.

### Value

A list is returned containing the ingredients below from M-GRAF2 model corresponding to the largest log-likelihood over iterations.

 `Z` A numeric vector containing the lower triangular entries in the estimated matrix Z. `Lambda` Kx1 vector storing the diagonal entries in Λ. `Q` VxKxn array containing the estimated VxK orthonormal matrix Q_i, i=1,...,n. `D_LT` Lxn matrix where each column stores the lower triangular entries in D_i = Q_i * Λ * Q_i^{\top}; L=V(V-1)/2. `LL_max` Maximum log-likelihood across iterations. `LL` Joint log-likelihood at each iteration.

### Examples

```data(A)
n = dim(A)[3]
subs = sample.int(n=n,size=30)
A_sub = A[ , , subs]
res = MGRAF2(A=A_sub, K=3, tol=0.01, maxit=5)

```

[Package CISE version 0.1.0 Index]