ghapca(lambda, U, x, gamma, q = length(lambda), center, sort = TRUE)
Arguments
lambda
optional vector of eigenvalues.
U
matrix of eigenvectors (PC) stored in columns.
x
new data vector.
gamma
vector of gain parameters.
q
number of eigenvectors to compute.
center
optional centering vector for x.
sort
Should the new eigenpairs be sorted?
Details
The vector gamma determines the weight placed on the new data in updating each eigenvector (the first coefficient of gamma corresponds to the first eigenvector, etc). It can be specified as a single positive number or as a vector of length ncol(U). Larger values of gamma place more weight on x and less on U. A common choice for (the components of) gamma is of the form c/n, with n the sample size and c a suitable positive constant.
If sort is TRUE and lambda is not missing, the updated eigenpairs are sorted by decreasing eigenvalue. Otherwise, they are not sorted.
Value
A list with components
values
updated eigenvalues or NULL.
vectors
updated eigenvectors.
References
Sanger (1989). Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Networks.
See Also
sgapca, snlpca
Examples
## Initialization
n <- 1e4 # sample size
n0 <- 5e3 # initial sample size
d <- 10 # number of variables
q <- d # number of PC
x <- matrix(runif(n*d), n, d)
x <- x %*% diag(sqrt(12*(1:d)))
# The eigenvalues of X are close to 1, 2, ..., d
# and the corresponding eigenvectors are close to
# the canonical basis of R^d
## GHA PCA
pca <- princomp(x[1:n0,])
xbar <- pca$center
pca <- list(values=pca$sdev[1:q]^2, vectors=pca$loadings[,1:q])
for (i in (n0+1):n) {
xbar <- updateMean(xbar, x[i,], i-1)
pca <- ghapca(pca$values, pca$vectors, x[i,], 2/i, q, xbar)
}