bsoipca: Block Stochastic Orthononal Iteration (BSOI)
| bsoipca | R Documentation |
Block Stochastic Orthononal Iteration (BSOI)
Description
The online PCA algorithm of Mitliagkas et al. (2013) is a block-wise stochastic variant of the classical power-method.
Usage
bsoipca(x, q, U, B, center, byrow = FALSE)
Arguments
x |
data matrix. |
q |
number of PC to compute. |
U |
matrix of initial PCs in columns (optional). |
B |
size of block updates (optional). |
center |
centering vector (optional). |
byrow |
are the data vectors in |
Details
The default value of B is floor(n/nblock) with n the number of data vectors in x, d the number of variables, and nblock=ceiling(log(d)) the number of blocks.
If U is specified, q defaults to ncol(U); otherwise the initial PCs are computed from the first block of data and q must be specified explicitly.
Although the algorithm does not give eigenvalues, they can easily be estimated by computing the variance of the data along the PCs.
Value
A matrix with the q first eigenvectors/PCs in columns.
References
Mitliagkas et al. (2013). Memory limited, streaming PCA. Advances in Neural Information Processing Systems.
Examples
## Simulate Brownian Motion
n <- 100 # number of sample paths
d <- 50 # number of observation points
x <- matrix(rnorm(n*d,sd=1/sqrt(d)),n,d)
x <- t(apply(x,1,cumsum)) # dim(x) = c(100,50)
q <- 10 # number of PC to compute
B <- 20 # block size
## BSOI PCA
U <- bsoipca(x, q, B=B, byrow=TRUE) # PCs
lambda <- apply(x %*% U, 2, var) # eigenvalues
