Description Usage Arguments Details Value Author(s) References Examples

Used for finding principal components of a numeric matrix. Missing values in the matrix are allowed. Principal Components are extracted one a time. The algorithm computes x = TP', where T is the 'scores' matrix and P is the 'loadings' matrix.

1 2 3 4 5 6 7 8 9 10 11 12 13 |

`x` |
Numerical matrix for which to find principal compontents. Missing values are allowed. |

`ncomp` |
Maximum number of principal components to extract from x. |

`center` |
If TRUE, subtract the mean from each column of x before PCA. |

`scale` |
if TRUE, divide the standard deviation from each column of x before PCA. |

`maxiter` |
Maximum number of NIPALS iterations for each principal component. |

`tol` |
Default 1e-9 tolerance for testing convergence of the NIPALS iterations for each principal component. |

`startcol` |
Determine the starting column of x for the iterations of each principal component. If 0, use the column of x that has maximum absolute sum. If a number, use that column of x. If a function, apply the function to each column of x and choose the column with the maximum value of the function. |

`fitted` |
Default FALSE. If TRUE, return the fitted (reconstructed) value of x. |

`force.na` |
Default FALSE. If TRUE, force the function to use the method for missing values, even if there are no missing values in x. |

`gramschmidt` |
Default TRUE. If TRUE, perform Gram-Schmidt orthogonalization at each iteration. |

`verbose` |
Default FALSE. Use TRUE or 1 to show some diagnostics. |

The R2 values that are reported are marginal, not cumulative.

A list with components `eig`

, `scores`

, `loadings`

,
`fitted`

, `ncomp`

, `R2`

, `iter`

, `center`

,
`scale`

.

Kevin Wright

Wold, H. (1966) Estimation of principal components and related models by iterative least squares. In Multivariate Analysis (Ed., P.R. Krishnaiah), Academic Press, NY, 391-420.

Andrecut, Mircea (2009). Parallel GPU implementation of iterative PCA algorithms. Journal of Computational Biology, 16, 1593-1599.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
B <- matrix(c(50, 67, 90, 98, 120,
55, 71, 93, 102, 129,
65, 76, 95, 105, 134,
50, 80, 102, 130, 138,
60, 82, 97, 135, 151,
65, 89, 106, 137, 153,
75, 95, 117, 133, 155), ncol=5, byrow=TRUE)
rownames(B) <- c("G1","G2","G3","G4","G5","G6","G7")
colnames(B) <- c("E1","E2","E3","E4","E5")
dim(B) # 7 x 5
p1 <- nipals(B)
dim(p1$scores) # 7 x 5
dim(p1$loadings) # 5 x 5
B2 = B
B2[1,1] = B2[2,2] = NA
p2 = nipals(B2, fitted=TRUE)
# Two ways to make a biplot
# method 1
biplot(p2$scores, p2$loadings)
# method 2
class(p2) <- "princomp"
p2$sdev <- sqrt(p2$eig)
biplot(p2, scale=0)
``` |

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