big_SVD: Partial SVD

View source: R/SVD.R

big_SVDR Documentation

Partial SVD


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.


  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))



An object of class FBM.


A function with parameters X, ind.row and ind.col, and that returns a data.frame with $center and $scale for the columns corresponding to ind.col, to scale each of their elements such as followed:

\frac{X_{i,j} - center_j}{scale_j}.

Default doesn't use any scaling. You can also provide your own center and scale by using as_scaling_fun().


An optional vector of the row indices that are used. If not specified, all rows are used. Don't use negative indices.


An optional vector of the column indices that are used. If not specified, all columns are used. Don't use negative indices.


Number of singular vectors/values to compute. Default is 10. This algorithm should be used to compute only a few singular vectors/values. If more is needed, have a look at


Maximum number of columns read at once. Default uses block_size.


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 then V = 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 then U = X \cdot V \cdot D^{-1},

  • if both dimensions are large, use big_randomSVD instead.


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




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)

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)
scores2 <- predict(test) # use this function to predict scores
all.equal(scores, scores2)
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)])

bigstatsr documentation built on Oct. 14, 2022, 9:05 a.m.