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Outlier Detection for Functional Data

Source: R/outliers.R
outliers.depth.pond.Rd

Functions for detecting outliers in functional data using depth measures. Outlier Detection using Weighted Depth

Usage

outliers.depth.pond(
  fdataobj,
  nb = 200,
  dfunc = depth.mode,
  threshold_method = c("quantile", "mad", "iqr"),
  quan = 0.05,
  k = NULL,
  ...
)

Arguments

fdataobj

An object of class 'fdata'.

nb

Number of bootstrap samples. Default is 200.

dfunc

Depth function to use. Default is depth.mode.

threshold_method

Method for computing the outlier threshold. Options:

"quantile"

Use quantile of weighted depths (default). Curves with depth below this quantile are flagged as outliers.

"mad"

Use median - k * MAD of weighted depths. More robust to existing outliers in the data.

"iqr"

Use Q1 - k * IQR, similar to boxplot whiskers.

quan

Quantile for outlier cutoff when threshold_method = "quantile". Default is 0.05, meaning curves with depth in the bottom 5% are flagged (95th percentile threshold). Lower values detect fewer outliers.

k

Multiplier for MAD or IQR methods. Default is 2.5 for MAD and 1.5 for IQR. Higher values detect fewer outliers.

...

Additional arguments passed to depth function.

Value

A list of class 'outliers.fdata' with components:

outliers

Indices of detected outliers

depths

Depth values for all curves

weighted_depths

Bootstrap-weighted depth values

cutoff

Depth cutoff used

threshold_method

Method used for threshold computation

fdataobj

Original fdata object

Details

Detects outliers based on depth with bootstrap resampling. The threshold for outlier detection can be computed using different methods.

The function first computes depth values for all curves, then uses bootstrap resampling to obtain weighted depths that are more robust to sampling variability.

Threshold Methods:

  • quantile: Flags curves with depth below the specified quantile. With quan = 0.1, approximately 10% of curves would be flagged under the null hypothesis of no outliers. Suitable when you expect a specific proportion of outliers.

  • mad: Uses median(depths) - k * MAD(depths) as threshold. More robust because MAD is not influenced by extreme values. With k = 2.5, this corresponds roughly to a 1-2% false positive rate under normality.

  • iqr: Uses Q1 - k * IQR as threshold, similar to boxplot outlier detection. With k = 1.5, corresponds to the standard boxplot fence.

Examples

# Create 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) + 3  # outlier
X[30, ] <- -sin(2*pi*t)     # outlier
fd <- fdata(X, argvals = t)

# Default: quantile method with 95th percentile (bottom 5%)
out1 <- outliers.depth.pond(fd, nb = 50)

# More permissive: bottom 10%
out1b <- outliers.depth.pond(fd, nb = 50, quan = 0.1)

# MAD method (more robust)
out2 <- outliers.depth.pond(fd, nb = 50, threshold_method = "mad", k = 2.5)

# IQR method (boxplot-like)
out3 <- outliers.depth.pond(fd, nb = 50, threshold_method = "iqr", k = 1.5)