redoASest: Re-estimate A, S matrix
In Lululuella/debCAM: Deconvolution by Convex Analysis of Mixtures

Description Usage Arguments Details Value Examples

This function re-estimates proportion and expression matrix iteratively by Alternating Least Square (ALS) method. The initial values are from markers or known proportion matrix or known expression matrix,

1 2	redoASest(data, MGlist, A = NULL, S = NULL, generalNMF = FALSE, maxIter = 2, methy = FALSE)

`data`	A data set that will be internally coerced into a matrix. Each row is a gene and each column is a sample. data should be in non-log linear space with non-negative numerical values (i.e. >= 0). Missing values are not supported. All-zero rows will be removed internally.
`MGlist`	A list of vectors, each of which contains CAM-detected markers and/or prior markers for one subpopulation.
`A`	Initial proportion matrix. If NULL, it will be estimated from initial expression matrix. If initial expression matrix is also NULL, it will be estimated from `MGlist` using `AfromMarkers`.
`S`	Initial expression matrix. If NULL, it will be estimated from initial proportion matrix.
`generalNMF`	If TRUE, the decomposed proportion matrix has no sum-to-one constraint for each row. Without this constraint, the scale ambiguity of each column vector in proportion matrix will not be removed. The default is FALSE.
`maxIter`	maximum number of iterations for Alternating Least Square (ALS) method. The default is 2. If zero, ALS is not applied.
`methy`	Should be TRUE when dealing with methylation data, whose expression levels are confined between 0 and 1.

If only markers are provided, they are used to estimate initial proportion matrix and then expression matrix. If proportion matrix or expression matrix is provided, it will be treated as initial matrix to estimate the other one. Then Alternating Least Square (ALS) method is applied to estimate two matrix alternatively. Note only markers' squared errors will be counted in ALS, which facilitates (1) faster computational running time and (2) a greater signal-to-noise ratio owing to markers' discriminatory power.

This function can be used to refine CAM estimation or perform supervised deconvolution. Note that allowing too many iterations may bring the risk of a significant deviation from initial values.

A list containing the following components:

`Aest`	Proportion matrix after re-estimation and possible refinement.
`Sest`	expression matrix after re-estimation and possible refinement.
`mse`	Mean squared error (i.e. mean of reconstruction errors) for input markers

#obtain data and run CAM
data(ratMix3)
data <- ratMix3$X
rCAM <- CAM(data, K = 3, dim.rdc= 3, thres.low = 0.30, thres.high = 0.95)
#obtain marker genes detected by CAM for estimating A
MGlist <- MGsforA(rCAM, K = 3)

#Re-estimation based on marker list
rre <- redoASest(data, MGlist, maxIter = 10)
Aest <- rre$Aest #re-estimated A matrix
Sest <- rre$Sest #re-estimated S matrix

#Re-estimation with initial A matrix
rre <- redoASest(data, MGlist, A=ratMix3$A, maxIter = 10)

#Re-estimation with initial S matrix
rre <- redoASest(data, MGlist, S=ratMix3$S, maxIter = 10)