Initialize Sigma and Omega using an initial clique of neighbors of the missing actor
initOmega.RdInitialize Sigma and Omega by taking the principal component of cliques as initial value for the hidden variables. The PCA is done on the correaltion matrix, the variance of hidden variables are set to the empirical variances of the pca. The corresponding precision term in omega is set to 1 for identifiability reasons.
initOmega(Sigma = NULL, cliqueList, cst = 1.1)
Arguments
| Sigma | variance-covariance matrix (p x p) |
|---|---|
| cliqueList | list of found cliques, given as vectorss of nodes indices |
| cst | small constant for positive definiteness |
Value
Sigma0: initial value of complete covariance matrix ((p+r)x(p+r) matrix)
K0: initial value of complete precision matrix ((p+r)x(p+r) matrix)
clique: vector containing the indices of the nodes in the clique
Examples
Sigma=data$Sigma initClique=FitSparsePCA(data$Y,r=1)$cliques initOmega(Sigma=Sigma, cliqueList=initClique)#> $Sigma0 #> [,1] [,2] [,3] [,4] [,5] [,6] #> [1,] 1.0000000 -0.6564880 0.3978100 0.4503413 0.1384223 -0.74370241 #> [2,] -0.6564880 1.0000000 -0.6059668 -0.6859855 -0.2108528 0.48823173 #> [3,] 0.3978100 -0.6059668 1.0000000 0.4156845 0.3479609 -0.29585224 #> [4,] 0.4503413 -0.6859855 0.4156845 1.0000000 0.1446420 -0.33491991 #> [5,] 0.1384223 -0.2108528 0.3479609 0.1446420 1.0000000 -0.10294502 #> [6,] -0.7437024 0.4882317 -0.2958522 -0.3349199 -0.1029450 1.00000000 #> [7,] -0.1006306 0.1532863 -0.2529615 -0.1051522 -0.7269825 0.07483923 #> [8,] 0.1384223 -0.2108528 0.3479609 0.1446420 0.3717361 -0.10294502 #> [9,] -0.1006306 0.1532863 -0.2529615 -0.1051522 -0.2702456 0.07483923 #> [10,] 0.1453388 -0.2213883 0.3653472 0.1518692 0.3903103 -0.10808880 #> [11,] 0.8301459 -0.8370341 0.5583875 0.9324889 0.3985596 -0.91375658 #> [,7] [,8] [,9] [,10] [,11] #> [1,] -0.10063061 0.1384223 -0.10063061 0.1453388 0.8301459 #> [2,] 0.15328628 -0.2108528 0.15328628 -0.2213883 -0.8370341 #> [3,] -0.25296150 0.3479609 -0.25296150 0.3653472 0.5583875 #> [4,] -0.10515217 0.1446420 -0.10515217 0.1518692 0.9324889 #> [5,] -0.72698251 0.3717361 -0.27024561 0.3903103 0.3985596 #> [6,] 0.07483923 -0.1029450 0.07483923 -0.1080888 -0.9137566 #> [7,] 1.00000000 -0.2702456 0.19646383 -0.2837488 -0.4404733 #> [8,] -0.27024561 1.0000000 -0.72698251 0.3903103 0.2525505 #> [9,] 0.19646383 -0.7269825 1.00000000 -0.2837488 -0.1835998 #> [10,] -0.28374878 0.3903103 -0.28374878 1.0000000 0.2651695 #> [11,] -0.44047331 0.2525505 -0.18359978 0.2651695 1.5156481 #> #> $K0 #> [,1] [,2] [,3] [,4] [,5] #> [1,] 2.995000e+00 1.153710e+00 -5.551115e-16 -1.443290e-15 1.174218e-16 #> [2,] 1.153710e+00 3.226510e+00 9.575898e-01 1.295721e+00 7.316634e-17 #> [3,] -8.065872e-17 9.575898e-01 1.850150e+00 4.937363e-16 -2.443984e-01 #> [4,] -1.539993e-15 1.295721e+00 -5.044652e-16 5.212917e+00 -1.474759e-16 #> [5,] -1.601693e-16 -8.166100e-17 -2.443984e-01 -6.348823e-16 2.432368e+00 #> [6,] 1.664111e+00 5.165756e-16 -1.282238e-16 -3.257295e+00 3.106197e-16 #> [7,] 3.515853e-16 2.813595e-16 3.898653e-16 -1.570168e+00 1.541862e+00 #> [8,] 7.210915e-17 -3.483550e-16 -2.443984e-01 -2.317723e-16 -2.802267e-01 #> [9,] 9.718497e-17 -8.456205e-17 -3.371215e-16 -1.169113e-16 -2.758972e-16 #> [10,] -3.475685e-17 5.794442e-17 -2.731656e-01 3.471644e-17 -3.132111e-01 #> [11,] 1.478934e-15 1.137663e-15 4.882736e-16 -4.911705e+00 3.637128e-16 #> [,6] [,7] [,8] [,9] [,10] #> [1,] 1.664111e+00 1.879141e-16 -1.922296e-17 -1.175983e-16 6.298948e-17 #> [2,] -1.272872e-15 -4.016447e-16 9.755512e-17 3.902567e-18 -7.316634e-17 #> [3,] -1.686729e-16 -1.885295e-17 -2.443984e-01 1.754450e-16 -2.731656e-01 #> [4,] -3.257295e+00 -1.570168e+00 3.188573e-16 1.351326e-16 1.729410e-16 #> [5,] 3.002154e-16 1.541862e+00 -2.802267e-01 -3.173433e-16 -3.132111e-01 #> [6,] 5.429464e+00 1.538626e+00 -3.691970e-16 -2.471415e-16 -8.225295e-17 #> [7,] 1.538626e+00 2.862596e+00 -5.139808e-16 -4.365212e-16 2.052234e-17 #> [8,] 8.150804e-17 -2.318175e-16 2.432368e+00 1.541862e+00 -3.132111e-01 #> [9,] 1.179954e-16 4.529421e-17 1.541862e+00 2.120907e+00 -7.913486e-17 #> [10,] -6.331278e-17 -1.778171e-16 -3.132111e-01 -3.956743e-16 1.344299e+00 #> [11,] 4.813036e+00 2.320108e+00 -5.343714e-16 -3.004692e-16 -2.410241e-16 #> [,11] #> [1,] 2.408360e-15 #> [2,] -6.523283e-16 #> [3,] -4.325448e-16 #> [4,] -4.911705e+00 #> [5,] 3.234955e-16 #> [6,] 4.813036e+00 #> [7,] 2.320108e+00 #> [8,] 4.166517e-17 #> [9,] 1.057285e-16 #> [10,] -4.430592e-17 #> [11,] 7.257622e+00 #> #> $cliquelist #> $cliquelist[[1]] #> [1] 4 6 7 #> #>
