Skip to contents

Principal Component Analysis (PCA)

Source: R/stats_fit_pca.R
pca.Rd

Fits an unsupervised Principal Component Analysis (PCA) model to a spectral data matrix. Model-internal centering and scaling are controlled via a ScalingStrategy object and do not modify the input matrix.

The default backend uses an internal NIPALS implementation. Alternatively, PCA algorithms from the pcaMethods package (e.g. "ppca", "svd", "robustPca") can be used.

Usage

pca(X, scaling, ncomp, method = "nipals")

Arguments

X

Numeric matrix (rows = samples, columns = variables).

scaling

A ScalingStrategy object defining model-internal centering and scaling (e.g. uv_scaling(center = TRUE)).

ncomp

Integer. Number of principal components to compute.

method

Character. PCA backend. Use "nipals" for the internal implementation or any method supported by pcaMethods::pca().

Value

An object of class m8_model with engine = "pca". The object contains:

  • fit$t: Score matrix (samples × components)

  • fit$p: Loading matrix (components × variables)

  • ctrl: Model control information (variance explained, scaling settings)

  • provenance: Attributes inherited from the input matrix

Details

PCA decomposes \(X\) into orthogonal score and loading matrices: $$X \approx T P$$ where:

  • \(T\) contains the principal component scores

  • \(P\) contains the loadings

The number of components is fixed by ncomp. Unlike supervised models, PCA does not use cross-validation or stopping rules.

Scaling and centering are applied internally during model fitting. The original input matrix is not modified.

See also

uv_scaling

Other modelling: opls(), pls()

Examples

data(covid)

uv <- uv_scaling(center=TRUE)
model <- pca(X=covid$X, scaling=uv, ncomp=2)

show(model)
#> 
#> m8_model <pca>
#> ----------------------------------------
#> Dimensions  : 10 samples x 27819 variables
#> Mode        : unsupervised
#> Preprocess  : center | UV 
#> Components  : 2
#> ----------------------------------------
#> Use summary() for performance metrics.
#> 
summary(model)
#> $perf
#>   comp       R2X   R2X_cum selected    fit
#> 1    1 0.3023058 0.3023058     TRUE fitted
#> 2    2 0.1898503 0.4921561     TRUE fitted
#> 
#> $engine
#> [1] "pca (nipals)"
#> 
#> $y_type
#> [1] "unsupervised"
#> 

Tx <- scores(model)
Px <- loadings(model)

t2 <- hotellingsT2(Tx)
ell <-ellipse2d(t2)

# scores plot
plot(Tx, asp = 1,
  col = as.factor(covid$an$type),
  xlim = range(c(Tx[1,], ell$x)),
  ylim = range(c(Tx[2,], ell$y))
 )
lines(ell$x, ell$y, col = "grey", lty=2)