PMD.cv  R Documentation 
Performs crossvalidation to select tuning parameters for rank1 PMD, the penalized matrix decomposition for a data matrix.
PMD.cv(
x,
type = c("standard", "ordered"),
sumabss = seq(0.1, 0.7, len = 10),
sumabsus = NULL,
lambda = NULL,
nfolds = 5,
niter = 5,
v = NULL,
chrom = NULL,
nuc = NULL,
trace = TRUE,
center = TRUE,
upos = FALSE,
uneg = FALSE,
vpos = FALSE,
vneg = FALSE
)
x 
Data matrix of dimension $n x p$, which can contain NA for missing values. 
type 
"standard" or "ordered": Do we want v to simply be sparse, or should it also be smooth? If the columns of x are ordered (e.g. CGH spots along a chromosome) then choose "ordered". Default is "standard". If "standard", then the PMD function will make use of sumabs OR sumabsu&sumabsv. If "ordered", then the function will make use of sumabsu and lambda. 
sumabss 
Used only if type is "standard". A vector of sumabs values to be used. Sumabs is a measure of sparsity for u and v vectors, between 0 and

sumabsus 
Used only for type "ordered". A vector of sumabsu values to be used. Sumabsu measures sparseness of u  it is the sum of absolute values of elements of u. Must be between 1 and sqrt(n). 
lambda 
Used only if type is "ordered". This is the tuning parameter for the fused lasso penalty on v, which takes the form $lambda v1 + lambda v_j  v(j1)$. $lambda$ must be nonnegative. If NULL, then it is chosen adaptively from the data. 
nfolds 
How many crossvalidation folds should be performed? Default is 5. 
niter 
How many iterations should be performed. For speed, only 5 are performed by default. 
v 
The first right singular vector(s) of the data. (If missing data is present, then the missing values are imputed before the singular vectors are calculated.) v is used as the initial value for the iterative PMD algorithm. If x is large, then this step can be timeconsuming; therefore, if PMD is to be run multiple times, then v should be computed once and saved. 
chrom 
If type is "ordered", then this gives the option to specify that some columns of x (corresponding to CGH spots) are on different chromosomes. Then v will be sparse, and smooth within each chromosome but not between chromosomes. Length of chrom should equal number of columns of x, and each entry in chrom should be a number corresponding to which chromosome the CGH spot is on. 
nuc 
If type is "ordered", can specify the nucleotide position of each CGH spot (column of x), to be used in plotting. If NULL, then it is assumed that CGH spots are equally spaced. 
trace 
Print out progress as iterations are performed? Default is TRUE. 
center 
Subtract out mean of x? Default is TRUE 
upos 
Constrain the elements of u to be positive? TRUE or FALSE. 
uneg 
Constrain the elements of u to be negative? TRUE or FALSE. 
vpos 
Constrain the elements of v to be positive? TRUE or FALSE. Cannot be used if type is "ordered". 
vneg 
Constrain the elements of v to be negative? TRUE or FALSE. Cannot be used if type is "ordered." 
If type is "standard", then lasso ($L_1$) penalties (promoting sparsity) are placed on u and v. If type is "ordered", then lasso penalty is placed on u and a fused lasso penalty (promoting sparsity and smoothness) is placed on v.
Crossvalidation of the rank1 PMD is performed over sumabss (if type is "standard") or over sumabsus (if type is "ordered"). If type is "ordered", then lambda is chosen from the data without crossvalidation.
The crossvalidation works as follows: Some percent of the elements of $x$ is removed at random from the data matrix. The PMD is performed for a range of tuning parameter values on this partiallymissing data matrix; then, missing values are imputed using the decomposition obtained. The value of the tuning parameter that results in the lowest sum of squared errors of the missing values if "best".
To do crossvalidation on the rank2 PMD, first the rank1 PMD should be computed, and then this function should be performed on the residuals, given by $xudv'$.
cv 
Average sum of squared errors obtained over crossvalidation folds. 
cv.error 
Standard error of average sum of squared errors obtained over crossvalidation folds. 
bestsumabs 
If type="standard", then value of sumabss resulting in smallest CV error is returned. 
bestsumabsu 
If type="ordered", then value of sumabsus resulting in smallest CV error is returned. 
v.init 
The first right singular vector(s) of the data; these are returned to save on computation time if PMD will be run again. 
Witten D. M., Tibshirani R., and Hastie, T. (2009)
A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis, Biostatistics, Gol 10 (3), 515534, Jul 2009
PMD, SPC
# See examples in PMD help file
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