| Title: | Structured Matrix Completion |
|---|---|
| Description: | Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. 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. |
| Authors: | Yifu Liu, Anru Zhang, Tianxi Cai, T. and Tony Cai |
| Maintainer: | Yifu Liu <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0 |
| Built: | 2025-02-14 04:40:45 UTC |
| Source: | https://github.com/yifuliu/structuremc |
Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. 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.
Yifu Liu and Anru Zhang
Maintainer: Yifu Liu ([email protected])
Cai, T., Cai, T. T., & Zhang, A. (2015). Structured Matrix Completion with Applications to Genomic Data Integration. Journal of the American Statistical Association.
This function returns the spectral norm of a real matrix if type is 2. Otherwise, it returns the matirx norm of the "norm" function using LAPACK.
mynorm(x, type = c("O", "I", "F", "M", "2"))mynorm(x, type = c("O", "I", "F", "M", "2"))
x |
numeric matrix |
type |
character string, specifying the type of matrix norm to be computed. Details see norm function in R base. |
Yifu Liu and Anru Zhang
Cai, T., Cai, T. T., & Zhang, A. (2015). Structured Matrix Completion with Applications to Genomic Data Integration. Journal of the American Statistical Association.
norm
A = matrix(rnorm(10, mean = 0, sd = 0.1), 10, 10) mynorm(A, "2") mynorm(A, "O")A = matrix(rnorm(10, mean = 0, sd = 0.1), 10, 10) mynorm(A, "2") mynorm(A, "O")
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)smc.FUN(A.mat, c_T, col_thresh, m1, m2)
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 |
Yifu Liu and Anru Zhang
Cai, T., Cai, T. T., & Zhang, A. (2015). Structured Matrix Completion with Applications to Genomic Data Integration. Journal of the American Statistical Association.
##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 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))) ##recovery the block A22 A22 = smc.FUN(Arecovery, 2, "True", m1, m2)##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 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))) ##recovery the block A22 A22 = smc.FUN(Arecovery, 2, "True", m1, m2)