BiCCA: Bi-order Canonical Correlation Analysis (BiCCA)

In KChen-lab/bindSC: Bi-order INtegration of Data from Single Cell multi-omics technologies \

Bi-order Canonical Correlation Analysis (BiCCA)

Description

Assuming there are two matrices X (M features by K samples) and Y (N features by L samples), we want to find the correlation in feature and sample levels between X and Y. Standard CCA could not handle this case because it requires that there should be at least one dimension shared by two datasets. The BiCCA function introudces one transition matrix Z (M features by L samples) to bridge X with Y. The transition matrix Z is solved by maximalizing correlation between (X, Z) in sample level and correlation between (Z, Y) in feature level simultaneously. Then sample/feature level correlation can be obtained by applying standard CCA on (X, Z) and (Y, Z), respectively.

Usage

BiCCA(
  X = NULL,
  Z0 = NULL,
  Y = NULL,
  X.clst = NULL,
  Y.clst = NULL,
  parameter.optimize = FALSE,
  alpha = NULL,
  lambda = NULL,
  K = 5,
  temp.path = NULL,
  num.iteration = 100,
  tolerance = 0.01,
  save = FALSE,
  block.size = 5000
)

Arguments

X	First matrix (M features by K samples)
Z0	Transition matrix (M features by L samples)
Y	Second matrix (N features by L samples)
X.clst	Cluster ID vector for the first matrix
Y.clst	Cluster ID vector for the second matrix
alpha	Couple coefficient to assign weight on initilized gene activity matrix Z0 [default 0.5]. alpha is set to [0 1). If alpha is set to 0, the initilized Z0 will not be involved after the 2nd iteration.
lambda	Couple coefficient to assign a weight factor to multi-objective function [default 0.5]. lambda is set to (0 1). If lambda is set to 0, the first modality will not be involved during the iteration process. If lambda is set to 1, the second modality will not be involved during the iteration process. In this case, biCCA will reduces to traditional CCA.
K	Number of canonical vectors to calculate in low-dimension space [default 10]
temp.path	Folder that is used to store temporary files. Only works when option save is set to be TRUE [default NULL]
num.iteration	Maximal number of iteration [default 100]
tolerance	Relative change ratio for frobenius norm of matrix Z during iteration [default 0.05]
save	Save the temporay files [default FALSE]
block.size	Sample/feature size for each block, only works when bigMemory is set to TRUE

Value

Returns the object with list:

* 'Z' - contains the estimated transition matrix (M features by L samples)

* 'u' - contains the canonical correlation vectors for X (K samples by K factor)

* 'r' - contains the canonical correlation vectors for Z (sample level)(L samples by K factor)

* 's' - contains the canonical correlation vectors for Z (feature level)(M features by K factor)

* 'v' - contains the canonical correlation vectors for Y (N features by K factor)

* 'delta' - relative change ratio for frobenius norm of matrix Z during iteration

Author(s)

Jinzhuang Dou, [e-mail] [e-mail]

Examples

X <- sim$X
Y <- sim$Y
Z0 <- sim$Z0

out <- BiCCA(X=X, Z0=Z0, Y=Y, 
      K = 5, X.clst =  sim$X_meta$Group,
      Y.clst =  sim$Y_meta$Group,
      alpha = 0.5,
      lambda = 0.5,
      num.iteration = 100, 
      temp.path = "./tp",
      tolerance = 0.01, 
      save = TRUE, 
      block.size = 500)

KChen-lab/bindSC documentation built on Sept. 29, 2022, 4:24 a.m.