simlr.Rdsimlr minimizes reconstruction error across related modalities. That is, simlr will reconstruct each modality matrix from a basis set derived from the other modalities. The basis set can be derived from SVD, ICA or a simple sum of basis representations. This function produces dataset-wide multivariate beta maps for each of the related matrices. The multivariate beta maps are regularized by user input matrices that encode relationships between variables. The idea is overall similar to canonical correlation analysis but generalizes the basis construction and to arbitrary numbers of modalities.
simlr(
voxmats,
smoothingMatrices,
iterations = 10,
sparsenessQuantiles,
positivities,
initialUMatrix,
mixAlg = c("svd", "ica", "avg", "rrpca-l", "rrpca-s", "pca", "stochastic"),
orthogonalize = FALSE,
repeatedMeasures = NA,
lineSearchRange = c(-1e+10, 1e+10),
lineSearchTolerance = 1e-08,
randomSeed,
constraint = c("Grassmannx1000x1000", "Stiefelx1000x1000", "orthox1000x1000", "none"),
energyType = c("cca", "regression", "normalized", "ucca", "lowRank",
"lowRankRegression"),
vmats,
connectors = NULL,
optimizationStyle = c("lineSearch", "mixed", "greedy"),
scale = c("centerAndScale", "sqrtnp", "np", "center", "norm", "none", "impute",
"eigenvalue", "robust", "whiten", "lowrank", "rank"),
expBeta = 0,
jointInitialization = TRUE,
sparsenessAlg = NA,
verbose = FALSE
)A list that contains the named matrices. Note: the optimization will likely perform much more smoothly if the input matrices are each scaled to zero mean unit variance e.g. by the scale function.
list of (sparse) matrices that allow parameter smoothing/regularization. These should be square and same order and size of input matrices.
number of gradient descent iterations
vector of quantiles to control sparseness - higher is sparser
vector that sets for each matrix if we restrict to positive or negative solution (beta) weights. choices are positive, negative or either as expressed as a string.
list of initialization matrix size n by k for each modality. Otherwise, pass a single scalar to control the
number of basis functions in which case random initialization occurs. One
may also pass a single initialization matrix to be used for all matrices.
If this is set to a scalar, or is missing, a random matrix will be used.
'svd', 'ica', 'rrpca-l', 'rrpca-s', 'stochastic', 'pca' or 'avg' denotes the algorithm employed when estimating the mixed modality bases
boolean to control whether we orthogonalize the solutions explicitly
list of repeated measurement identifiers. this will allow estimates of per identifier intercept.
lower and upper limit used in optimize
tolerance used in optimize, will be multiplied by each matrix norm such that it scales appropriately with input data
controls repeatability of ica-based decomposition
one of none, Grassmann, GrassmannInv or Stiefel
one of regression, normalized, lowRank, cca or ucca
optional initial v matrix list
a list ( length of projections or number of modalities ) that indicates which modalities should be paired with current modality
one of c("mixed","greedy","linesearch")
options to standardize each matrix. e.g. divide by the square root of its number of variables (Westerhuis, Kourti, and MacGregor 1998), divide by the number of variables or center or center and scale or ... (see code). can be a vector which will apply each strategy in order.
if greater than zero, use exponential moving average on gradient.
boolean for initialization options, default TRUE
NA is default otherwise basic, spmp or orthorank
boolean to control verbosity of output - set to level 2
in order to see more output, specifically the gradient descent parameters.
A list of u, x, y, z etc related matrices.
if (FALSE) { # \dontrun{
set.seed(1500)
nsub <- 25
npix <- c(100, 200, 133)
nk <- 5
outcome <- matrix(rnorm(nsub * nk), ncol = nk)
outcome1 <- matrix(rnorm(nsub * nk), ncol = nk)
outcome2 <- matrix(rnorm(nsub * nk), ncol = nk)
outcome3 <- matrix(rnorm(nsub * nk), ncol = nk)
view1tx <- matrix(rnorm(npix[1] * nk), nrow = nk)
view2tx <- matrix(rnorm(npix[2] * nk), nrow = nk)
view3tx <- matrix(rnorm(npix[3] * nk), nrow = nk)
mat1 <- (outcome %*% t(outcome1) %*% (outcome1)) %*% view1tx
mat2 <- (outcome %*% t(outcome2) %*% (outcome2)) %*% view2tx
mat3 <- (outcome %*% t(outcome3) %*% (outcome3)) %*% view3tx
matlist <- list(vox = mat1, vox2 = mat2, vox3 = mat3)
result <- simlr(matlist)
p1 <- mat1 %*% (result$v[[1]])
p2 <- mat2 %*% (result$v[[2]])
p3 <- mat3 %*% (result$v[[3]])
regs <- regularizeSimlr(matlist)
result2 <- simlr(matlist)
pred1 <- predictSimlr(matlist, result)
pred2 <- predictSimlr(matlist, result2)
# compare to permuted data
s1 <- sample(1:nsub)
s2 <- sample(1:nsub)
resultp <- simlr(list(vox = mat1, vox2 = mat2[s1, ], vox3 = mat3[s2, ]))
p1p <- mat1 %*% (resultp$v[[1]])
p2p <- mat2[s1, ] %*% (resultp$v[[2]])
p3p <- mat3[s2, ] %*% (resultp$v[[3]])
# compare to SVD
svd1 <- svd(mat1, nu = nk, nv = 0)$u
svd2 <- svd(mat2, nu = nk, nv = 0)$u
svd3 <- svd(mat3, nu = nk, nv = 0)$u
# real
range(cor(p1, p2))
range(cor(p1, p3))
range(cor(p3, p2))
# permuted
range(cor(p1p, p2p))
range(cor(p1p, p3p))
range(cor(p3p, p2p))
# svd
print(range(cor(svd1, svd2)))
resultp <- simlr(list(vox = mat1, vox2 = mat2[s1, ], vox3 = mat3[s2, ]),
initialUMatrix = nk, verbose = TRUE, iterations = 5,
energyType = "normalized"
)
} # }