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Magnitude-Shape Outlier Detection for Functional Data

Source: R/outliers.R
magnitudeshape.Rd

Performs Magnitude-Shape (MS) outlier detection for functional data. Each curve is represented as a point in 2D space where the x-axis represents magnitude outlyingness and the y-axis represents shape outlyingness.

Usage

magnitudeshape(
  fdataobj,
  depth.func = depth.MBD,
  cutoff.quantile = 0.993,
  col.normal = "black",
  col.outliers = "red",
  label = "index",
  label_all = FALSE,
  ...
)

Arguments

fdataobj

An object of class 'fdata'.

depth.func

Depth function to use for computing outlyingness. Default is depth.MBD.

cutoff.quantile

Quantile for outlier cutoff (default 0.993).

col.normal

Color for normal curves (default "black").

col.outliers

Color for outlier curves (default "red").

label

What to use for labeling outlier points. Options:

  • "index": Use numeric indices (default)

  • "id": Use observation IDs from the fdata object

  • A column name from the fdata metadata (e.g., "patient_id")

  • NULL: No labels

label_all

Logical. If TRUE, label all points, not just outliers. Default FALSE.

...

Additional arguments passed to depth function.

Value

A list of class 'magnitudeshape' with components:

MO

Magnitude outlyingness values

VO

Shape (variability) outlyingness values

outliers

Indices of detected outliers

cutoff

Chi-squared cutoff value used

plot

The ggplot object

Details

The MS plot (Dai & Genton, 2019) decomposes functional outlyingness into:

  • Magnitude Outlyingness (MO): Based on pointwise median of directional outlyingness - captures shift outliers

  • Shape Outlyingness (VO): Based on variability of directional outlyingness - captures shape outliers

Outliers are detected using the chi-squared distribution with cutoff at the specified quantile.

References

Dai, W. and Genton, M.G. (2019). Directional outlyingness for multivariate functional data. Computational Statistics & Data Analysis, 131, 50-65.

Examples

# Create functional data with outliers
set.seed(42)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 30, 50)
for (i in 1:28) X[i, ] <- sin(2*pi*t) + rnorm(50, sd = 0.2)
X[29, ] <- sin(2*pi*t) + 2  # Magnitude outlier
X[30, ] <- sin(4*pi*t)       # Shape outlier
fd <- fdata(X, argvals = t)

# Create MS plot
ms <- magnitudeshape(fd)

# With IDs and metadata
fd <- fdata(X, argvals = t, id = paste0("curve_", 1:30))
ms <- magnitudeshape(fd, label = "id")