smc.FUN {StructureMC}

Structured Matrix Completion

Description

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.

Usage

smc.FUN(A.mat, c_T, row_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.

row_thresh

is row thresholding

m1

number of rows of block A11

m2

number of columns of block A11

Value

smc.FUN()

returns the missing block of initial input matrix which has the following components:

A.mat

the approximately low-rank matrix with given value of other three blocks and NA values for the block that user want to recover.

c_T

is the thresholding level, the default value is 2.

row_thresh

it is the row thresholding which is "True" under default. Otherwise, it can be "False" to make it column thresholding.

m1

number of rows of block A11. It can be used to calculate the rest of dimension of blocks in A.mat with m2.

m2

number of columns of block A11. It can be used to calculate the rest of dimension of blocks in A.mat with m1.

Author(s)

Yifu Liu and Anru Zhang

References

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

Examples

#dimension of matrix A with row number p1 = 10 and column number p2 = 9
p1 = 60
p2 = 50
m1 = 55 #row number of A11
m2 = 45 #column number of A11
A = matrix(rnorm(300, mean = 0.05, sd = 0.1), p1, p2)

#different blocks of our matrix A that are used to approximate missing block A22
A11 = A[1:m1, 1:m2]
A12 = A[1:m1, (1+m2):p2]
A21 = A[(1+m1):p1, 1:m2]
Arecovery = rbind(cbind(A11,A12),cbind(A21,matrix(NA,nrow=p1-m1,ncol=p2-m2)))

#recover the missing block A22 where A22 is now filled with approximate values by our algorithm.
A22 = smc.FUN(Arecovery, 2, "True", m1, m2)