big_SVD {bigstatsr} | R Documentation |
Partial SVD
Description
An algorithm for partial SVD (or PCA) of a Filebacked Big Matrix through the eigen decomposition of the covariance between variables (primal) or observations (dual). Use this algorithm only if there is one dimension that is much smaller than the other. Otherwise use big_randomSVD.
Usage
big_SVD(
X,
fun.scaling = big_scale(center = FALSE, scale = FALSE),
ind.row = rows_along(X),
ind.col = cols_along(X),
k = 10,
block.size = block_size(nrow(X))
)
Arguments
X |
An object of class FBM. |
fun.scaling |
A function with parameters
Default doesn't use any scaling.
You can also provide your own |
ind.row |
An optional vector of the row indices that are used. If not specified, all rows are used. Don't use negative indices. |
ind.col |
An optional vector of the column indices that are used. If not specified, all columns are used. Don't use negative indices. |
k |
Number of singular vectors/values to compute. Default is |
block.size |
Maximum number of columns read at once. Default uses block_size. |
Details
To get X = U \cdot D \cdot V^T
,
if the number of observations is small, this function computes
K_(2) = X \cdot X^T \approx U \cdot D^2 \cdot U^T
and thenV = X^T \cdot U \cdot D^{-1}
,if the number of variable is small, this function computes
K_(1) = X^T \cdot X \approx V \cdot D^2 \cdot V^T
and thenU = X \cdot V \cdot D^{-1}
,if both dimensions are large, use big_randomSVD instead.
Value
A named list (an S3 class "big_SVD") of
-
d
, the singular values, -
u
, the left singular vectors, -
v
, the right singular vectors, -
center
, the centering vector, -
scale
, the scaling vector.
Note that to obtain the Principal Components, you must use predict on the result. See examples.
Matrix parallelization
Large matrix computations are made block-wise and won't be parallelized
in order to not have to reduce the size of these blocks.
Instead, you may use Microsoft R Open
or OpenBLAS in order to accelerate these block matrix computations.
You can also control the number of cores used with
bigparallelr::set_blas_ncores()
.
See Also
Examples
set.seed(1)
X <- big_attachExtdata()
n <- nrow(X)
# Using only half of the data
ind <- sort(sample(n, n/2))
test <- big_SVD(X, fun.scaling = big_scale(), ind.row = ind)
str(test)
plot(test$u)
pca <- prcomp(X[ind, ], center = TRUE, scale. = TRUE)
# same scaling
all.equal(test$center, pca$center)
all.equal(test$scale, pca$scale)
# scores and loadings are the same or opposite
# except for last eigenvalue which is equal to 0
# due to centering of columns
scores <- test$u %*% diag(test$d)
class(test)
scores2 <- predict(test) # use this function to predict scores
all.equal(scores, scores2)
dim(scores)
dim(pca$x)
tail(pca$sdev)
plot(scores2, pca$x[, 1:ncol(scores2)])
plot(test$v[1:100, ], pca$rotation[1:100, 1:ncol(scores2)])
# projecting on new data
X2 <- sweep(sweep(X[-ind, ], 2, test$center, '-'), 2, test$scale, '/')
scores.test <- X2 %*% test$v
ind2 <- setdiff(rows_along(X), ind)
scores.test2 <- predict(test, X, ind.row = ind2) # use this
all.equal(scores.test, scores.test2)
scores.test3 <- predict(pca, X[-ind, ])
plot(scores.test2, scores.test3[, 1:ncol(scores.test2)])