fdars (version 0.3.3)

outliergram: Outliergram for Functional Data

Description

Creates an outliergram plot that displays MEI (Modified Epigraph Index) versus MBD (Modified Band Depth) for outlier detection. Points below the parabolic boundary are identified as outliers, and each outlier is classified by type.

Usage

outliergram(fdataobj, factor = 1.5, mei_threshold = 0.25, ...)

Value

An object of class 'outliergram' with components:

fdataobj

The input functional data

mei

MEI values for each curve

mbd

MBD values for each curve

outliers

Indices of detected outliers

outlier_type

Character vector of outlier types ("shape") for each detected outlier

n_outliers

Number of outliers detected

factor

The factor used for threshold adjustment

parabola

Coefficients of the parabolic boundary (a0, a1, a2)

threshold

The boxplot-fence threshold for distance below the parabola

dist_to_parabola

Vertical distance below the parabola for each curve (positive values indicate the point is below the parabola)

Arguments

fdataobj

An object of class 'fdata'.

factor

Factor to adjust the outlier detection threshold. Higher values make detection less sensitive. Default is 1.5.

mei_threshold

Deprecated and ignored. Kept for backwards compatibility.

...

Additional arguments (currently ignored).

Details

The outliergram plots MEI on the x-axis versus MBD on the y-axis. For a sample of size \(n\), the theoretical relationship is bounded by the finite-sample parabola (Arribas-Gil & Romo, 2014, Proposition 1): $$MBD \le a_0 + a_1 \cdot MEI + a_2 \cdot MEI^2$$ where \(a_0 = -2/(n(n-1))\), \(a_1 = 2(n+1)/(n-1)\), \(a_2 = -2(n+1)/(n-1)\).

Shape outliers are detected using a boxplot fence on the vertical distances below the parabola: a curve is flagged when its distance exceeds \(Q_3 + \mathrm{factor} \times IQR\).

References

Arribas-Gil, A. and Romo, J. (2014). Shape outlier detection and visualization for functional data: the outliergram. Biostatistics, 15(4), 603-619.

See Also

depth for depth computation, magnitudeshape for an alternative outlier visualization.

Examples

# Create functional data with different outlier types
set.seed(42)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 32, 50)
for (i in 1:29) X[i, ] <- sin(2 * pi * t) + rnorm(50, sd = 0.2)
X[30, ] <- sin(2 * pi * t) + 2       # magnitude outlier (high)
X[31, ] <- sin(2 * pi * t) - 2       # magnitude outlier (low)
X[32, ] <- sin(4 * pi * t)           # shape outlier
fd <- fdata(X, argvals = t)

# Create outliergram
og <- outliergram(fd)
print(og)
plot(og, color_by_type = TRUE)