Evaluate performance of PC estimates

Evaluate performance of PC estimates compared to true PC values

Usage

perfMetric(U, U_est, k = ncol(U_est), metric = c("MEV", "minSSE"))

Arguments

U

true eigen values

U_est

estimated eigen-values

k

number of PCs to evaluate

metric

evaluate the accuracy of the estimated PCs compared to the true PCs using mean explained variance ("MEV") or minimum of sum of squared errors ("minSSE")

Value

performance metric

Details

See performance metrics described by Li, et al. (2023)

References

• Li, Z., Meisner, J., & Albrechtsen, A. (2023). Fast and accurate out-of-core PCA framework for large scale biobank data. Genome Research, 33(9), 1599-1608. doi:10.1101/gr.277525.122 .

Examples

hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, `+`) }
 X <- hilbert(9)[, 1:6]
k = 4

# Compute SVD using two methods
dcmp <- svd( scale(X), k, k)
res <- PCAstream( X, k=k)
#> Scale and centering...
#> 
Epoch 0 / 7  
Epoch 1 / 7  
Epoch 2 / 7  
Epoch 3 / 7  
Epoch 4 / 7  
Epoch 5 / 7  
Epoch 6 / 7  
Epoch 7 / 7  
Final decompositions
Completed            

# Mean variance explained is 1
perfMetric(dcmp$u, res$u, metric = "MEV")
#> [1] 1

# minimum of sum of squared errors zero
perfMetric(dcmp$u, res$u, metric = "minSSE")
#> [1] 4.354012e-27