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In this post, I compare different approaches to get first principal components of large matrices in R.
Comparison
library(bigstatsr)
library(tidyverse)
Data
# Create two matrices, one with some structure, one without
n < 20e3
seq_m < c(1e3, 3e3, 10e3)
sizes < seq_along(seq_m)
X < E < list()
for (i in sizes) {
m < seq_m[i]
U < matrix(0, n, 10); U[] < rnorm(length(U))
V < matrix(0, m, 10); V[] < rnorm(length(V))
E[[i]] < matrix(rnorm(n * m), n, m)
X[[i]] < tcrossprod(U, V) + E[[i]]
}
I use matrices of different sizes. Some are structured with 10 hidden components, and some with only random data.
Optimized math library
I linked my R installation with OpenBLAS, an optimized parallel matrix library.
(NCORES < RhpcBLASctl::get_num_cores())
## [1] 6
RhpcBLASctl::blas_set_num_threads(NCORES)
## detected function goto_set_num_threads
Compared methods
models < tribble(
~method, ~fun, ~params,
"bigstatsr  1 core", bigstatsr::big_randomSVD, list(k = 10),
"bigstatsr  6 cores", bigstatsr::big_randomSVD, list(k = 10, ncores = NCORES),
"Rspectra", RSpectra::svds, list(k = 10),
"irlba", irlba::irlba, list(nv = 10, nu = 10),
"svd", svd::propack.svd, list(neig = 10),
"rsvd", rsvd::rsvd, list(k = 10)
) %>%
mutate(size = list(sizes), structured = list(c(TRUE, FALSE))) %>%
unnest(size, .drop = FALSE) %>%
unnest(structured, .drop = FALSE) %>%
mutate(user_time = NA, real_time = NA, pcs = list(NA))
Computing
# Filling this data frame with times and PC scores for each method and dataset
for (i in rows_along(models)) {
mat < `if`(models$structured[[i]], X, E)[[models$size[[i]]]]
time < system.time({
if (grepl("bigstatsr", models$method[[i]])) mat < as_FBM(mat)
res < do.call(models$fun[[i]], args = c(list(mat), models$params[[i]]))
})
models[["user_time"]][[i]] < time[1]
models[["real_time"]][[i]] < time[3]
models[["pcs"]][[i]] < res
}
## Warning in (function (X, neig = min(m, n), opts = list()) : Only 4 singular triplets converged
## within 50 iterations.
## Warning in (function (X, neig = min(m, n), opts = list()) : Only 5 singular triplets converged
## within 50 iterations.
## Warning in (function (X, neig = min(m, n), opts = list()) : Only 5 singular triplets converged
## within 50 iterations.
models < mutate(models, size = seq_m[size])
Timings
models %>%
ggplot(aes(size / 1000, real_time, color = method)) +
theme_bigstatsr() +
geom_point(cex = 6) +
geom_line(aes(linetype = method), lwd = 2) +
facet_grid(structured ~ ., scales = "free") +
theme(legend.position = c(0.25, 0.87),
legend.key.width = unit(6, "line")) +
labs(x = sprintf("ncol (x1000) (nrow = %d)", n), y = "Time (in seconds)",
color = "Methods:", linetype = "Methods:")
models %>%
filter(size == max(seq_m)) %>%
select(method, structured, user_time, real_time)
## # A tibble: 12 x 4
## method structured user_time real_time
##
## 1 bigstatsr  1 core TRUE 8.10 8.68
## 2 bigstatsr  1 core FALSE 106. 107.
## 3 bigstatsr  6 cores TRUE 0.456 6.80
## 4 bigstatsr  6 cores FALSE 0.616 45.3
## 5 Rspectra TRUE 17.9 3.39
## 6 Rspectra FALSE 329. 56.1
## 7 irlba TRUE 16.3 3.09
## 8 irlba FALSE 399. 68.8
## 9 svd TRUE 34.2 6.11
## 10 svd FALSE 274. 46.9
## 11 rsvd TRUE 4.12 3.89
## 12 rsvd FALSE 4.06 3.88
Errors
true1 < svd(X[[1]], nu = 10, nv = 10)
true2 < svd(E[[1]], nu = 10, nv = 10)
bdiff < function(x, y) {
if (ncol(x) < ncol(y)) return(Inf)
s = sign(x[1, ] / y[1, ])
max(apply(sweep(x, 2, s, '*')  y, 2, crossprod))
}
models %>%
filter(size == min(seq_m)) %>%
mutate(error = map2_dbl(structured, pcs, ~{
true < `if`(.x, true1, true2)
bdiff(.y$u, true$u)
})) %>%
select(method, structured, error)
## # A tibble: 12 x 3
## method structured error
##
## 1 bigstatsr  1 core TRUE 1.63e27
## 2 bigstatsr  1 core FALSE 1.08e 5
## 3 bigstatsr  6 cores TRUE 1.29e27
## 4 bigstatsr  6 cores FALSE 1.08e 5
## 5 Rspectra TRUE 1.63e27
## 6 Rspectra FALSE 3.07e18
## 7 irlba TRUE 9.06e26
## 8 irlba FALSE 1.78e 7
## 9 svd TRUE 6.83e27
## 10 svd FALSE Inf
## 11 rsvd TRUE 7.02e13
## 12 rsvd FALSE 2.38e+ 0
Conclusion

Packages {rsvd} and {svd} don’t give results precise enough when data is not structured.

Packages {bigstatsr} and {irlba} are less precise (but precise enough!) than {RSpectra} because of a different tolerance parameter they use.

Package {bigstatsr} is as fast as the other packages while not relying on matrix operations (see user timings above). So, even if you don’t have your R installation linked to some optimized math library, you would get the same performance. On the contrary, the other methods would likely be much slower if not using such optimized library.
So, I highly recommend using package {RSpectra} to compute first principal components, because it is very fast and precise. Moreover, it works with e.g. sparse matrices. Yet, If you have very large matrices or no optimized math library, I would recommend to use my package {bigstatsr} that internally uses {RSpectra} but implements parallel matrixvector multiplication in Rcpp for its data format stored on disk. To learn more on other features of R package {bigstatsr}, please have a look at the package website.
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