smooth matrix prediction

Reconstruct a n by p matrix given n by k basis functions or predictors. The reconstruction can be regularized. # norm( x - uv^t ) # d/dv ... leads to ( -u, x - uv^t ) # u^t u v^t - u^t x

smoothMatrixPrediction(
  x,
  basisDf,
  modelFormula = as.formula(" x ~ ."),
  iterations = 10,
  gamma = 0.000001,
  sparsenessQuantile = 0.5,
  positivity = c("positive", "negative", "either"),
  smoothingMatrix = NA,
  repeatedMeasures = NA,
  rowWeights = NA,
  LRR = NA,
  doOrth = FALSE,
  verbose = FALSE
)

Arguments

x	input matrix to be predicted.
basisDf	data frame for basis predictors
modelFormula	a formula object which has, on the left, the variable x and the prediction formula on the right.
iterations	number of gradient descent iterations
gamma	step size for gradient descent
sparsenessQuantile	quantile to control sparseness - higher is sparser.
positivity	restrict to positive or negative solution (beta) weights. choices are positive, negative or either as expressed as a string.
smoothingMatrix	allows parameter smoothing, should be square and same size as input matrix
repeatedMeasures	list of repeated measurement identifiers. this will allow estimates of per identifier intercept.
rowWeights	vectors of weights with size n (assumes diagonal covariance)
LRR	integer value sets rank for fast version exploiting matrix approximation
doOrth	boolean enforce gram-schmidt orthonormality
verbose	boolean option

Value

matrix of size p by k is output

Examples

if (FALSE) {
mask = getMask( antsImageRead( getANTsRData( 'r16' ) ) )
spatmat = t( imageDomainToSpatialMatrix( mask, mask ) )
smoomat = knnSmoothingMatrix( spatmat, k = 5, sigma = 1.0 )
mat <- matrix(rnorm(sum(mask)*50),ncol=sum(mask),nrow=50)
mat[ 1:25,100:10000]=mat[ 1:25,100:10000]+1
age = rnorm( 1:nrow(mat))
for ( i in c( 5000:6000, 10000:11000, 16000:17000 )  ){
  mat[ , i ] = age*0.1 + mat[,i]
  }
gen = c( rep("M",25), rep("F",12 ) , rep("T",13 ) )
repmeas = rep( c("A","B","C","D","E","F","G"), nrow( mat ) )[1:nrow(mat)]
mydf = data.frame( age = scale( age ), gen = gen )
fit = smoothMatrixPrediction( x=mat, basisDf=mydf, iterations = 10,
  gamma = 1.e-6, sparsenessQuantile = 0.5,
  smoothingMatrix = smoomat, repeatedMeasures=repmeas,
  verbose=T )
tt = mat %*% fit$v
print( cor.test( mydf$age, tt[,1] ) )
print( cor.test( fit$u[,"genM"], tt[,2] ) )
vimg = makeImage( mask, (fit$v[,1] ) ); print(range(vimg)*10)
plot( mask, vimg, window.overlay=range(abs(vimg)))
vimg = makeImage( mask, (fit$v[,2] ) ); print(range(vimg)*10)
plot( mask, vimg, window.overlay=range(abs(vimg)))
}