Structured Matrix Completion

The main function in our package, smc.FUN, is for recovery of the missing block A22 of an approximately low-rank matrix A given the other blocks A11, A12, A21.

smc.FUN(A.mat, c_T, col_thresh, m1, m2)

Arguments

A.mat	The approximately low-rank matrix that we want to recover
c_T	c_T is the thresholding level, the default value is 2.
col_thresh	is column thresholding
m1	number of rows of block A11
m2	number of columns of block A11

References

Cai, T., Cai, T. T., & Zhang, A. (2015). Structured Matrix Completion with Applications to Genomic Data Integration. Journal of the American Statistical Association.

Author

Yifu Liu, Anru Zhang, Tianxi Cai and T. Tony Cai,

Examples

##dimension of matrix A with row number p1 = 10 and column number p2 = 9
p1 = 10
p2 = 9
m1 = 6##row number of A11
m2 = 3##column number of A11
A = matrix(rnorm(10, mean = 0, sd = 0.1), p1, p2)
##find the approximation low-rank of A under singular value decomposition (SVD)
j1 = svd(A)$d
num<-length(which(j1!=0))
j2 = svd(A)$u
j3 = svd(A)$v
D<-diag(j1)
D[num, num] = 0
app_low_rank_A = j2
##consturct the matrix Arecovery that need to be recovered
A11 = app_low_rank_A[1:m1, 1:m2]
A12 = app_low_rank_A[1:m1, (1+m2):p2]
A21 = app_low_rank_A[(1+m1):p1, 1:m2]
Arecovery = rbind(cbind(A11,A12),cbind(A21,matrix(NA,nrow=p1-m1,ncol=p2-m2)))
##recovery the block A22
A22 = smc.FUN(Arecovery, 2, "True", m1, m2)