tvd_mss {fdaoutlier}

Outlier detection using the total variation depth and modified shape similarity index.

Description

Find shape and magnitude outliers using the Total Variation Depth and Modified Shape Similarity Index proposed in Huang and Sun (2019) doi:10.1080/00401706.2019.1574241.

Usage

tvd_mss(
  data,
  emp_factor_mss = 1.5,
  emp_factor_tvd = 1.5,
  central_region_tvd = 0.5
)

tvdmss(
  dts,
  emp_factor_mss = 1.5,
  emp_factor_tvd = 1.5,
  central_region_tvd = 0.5
)

Arguments

emp_factor_mss

The empirical factor of the classical boxplot used on the modified shape similarity index. Defaults to 1.5.

emp_factor_tvd

The empirical factor of the functional boxplot used on the TVD of observations. Defaults to 1.5.

central_region_tvd

A number between 0 and 1 indicating the central region probability of the functional boxplot used on the TVD of the observations. Defaults to 0.5. See also details.

dts, data

A matrix or dataframe of size n observations/curves by p domain/evaluation points.

Details

This method uses a combination of total variation depth (TVD) and modified shape similarity (MSS) index defined in Huang and Sun (2019) doi:10.1080/00401706.2019.1574241 to find magnitude and shape outliers. The TVD and MSS of all the observations are first computed and a classical boxplot is then applied on the MSS. Outliers detected by the boxplot of MSS are flagged as shape outliers. The shape outliers are then removed from the data and the TVD of the remaining observations are used in a functional boxplot to detect magnitude outliers. The central region of this functional boxplot (central_region_tvd) is w.r.t. to the original number of curves. Thus if 8 shape outliers are found out of 100 curves, specifying central_region_tvd = 0.5 will ensure that 50 observations are used as the central region in the functional boxplot on the remaining 92 observations.

Value

Returns a list containing the following

outliers

the indices of the (shape and magnitude) outliers

shape_outliers

the indices of the shape outliers

magnitude_outliers

the indices of the magnitude outliers

tvd

the total variation depths of the observations of data

mss

the modified shape similarity index of the observations of data

Functions

• tvd_mss(): Deprecated function. Use tvdmss instead.

Author(s)

Oluwasegun Ojo

References

Huang, H., & Sun, Y. (2019). A decomposition of total variation depth for understanding functional outliers. Technometrics, 61(4), 445-458.

See Also

msplot for outlier detection using msplot.

Examples

dt6 <- simulation_model6()
res <- tvdmss(dt6$data)
res$outliers