Outlier map from a projection or principal component analysis

Draw an outlier map showing the score distance and orthogonal distance of each observation from a projection or principal component analysis. The score distance measures how far an observation lies from the centre within the projection subspace, while the orthogonal distance measures how far it lies from the subspace. Pass object (the output of stats::prcomp() or an rrcov Pca* function); otherwise supply scores and loadings together with the original data. For a prcomp object, use its rank. argument to set the number of retained components.

When object is a PCA-like object and show_thresholds = TRUE, the score-distance and orthogonal-distance cutoffs are drawn as dashed lines and observations are coloured by type:

Regular observation: small score and orthogonal distance.
Good leverage point: large score distance, small orthogonal distance.
Orthogonal outlier: small score distance, large orthogonal distance.
Bad leverage point: large score and orthogonal distance.

The cutoffs are only defined for PCA-like objects, so show_thresholds is ignored when scores and loadings are passed directly.

Usage

outlier_map(
  object = NULL,
  data = NULL,
  scores = NULL,
  loadings = NULL,
  show_thresholds = TRUE,
  ...
)

Arguments

object: Optionally, the output of stats::prcomp() or an rrcov Pca* function. For a prcomp object, set the number of retained components with its rank. argument. If supplied, the scores and loadings arguments are ignored.
data: The original data matrix or data frame used to compute the projection, scaled if the projection was computed on scaled data. This is required to compute the orthogonal distances, except when object is a rrcov Pca* object (which stores them).
scores: A matrix or data frame of scores, with one column per retained component. Ignored if object is supplied.
loadings: A matrix or data frame of loadings, with one column per retained component. Ignored if object is supplied.
show_thresholds: If TRUE (the default) and object is a PCA-like object, the score-distance and orthogonal-distance cutoffs are drawn as dashed lines and observations are coloured by type. Ignored when scores and loadings are passed directly.
...: Additional arguments passed to ggplot2::geom_point().

Value

A ggplot object.

References

Hyndman, R J (2026) "That's weird: Anomaly detection using R", Chapter 9, https://OTexts.com/weird/.

Author

Rob J Hyndman

Examples

Y <- oldfaithful[, c("duration", "waiting")]
prcomp(Y, scale = TRUE, rank. = 1) |>
  outlier_map(data = Y)