Package {outliersHD}

Type: Package
Title: Detection of Outliers in High Dimensional Data
Version: 1.0
Date: 2026-06-29
Author: Michail Tsagris [aut, cre]
Maintainer: Michail Tsagris <mtsagris@uoc.gr>
Depends: R (≥ 4.0)
Imports: Rfast, Rfast2, Rnanoflann, stats
Description: Algorithms to detect high-dimensional outliers. The minimum diagonal product of Ro, Zou, Wang and Yin (2015) <doi:10.1093/biomet/asv021>, the algorithm of Wilkinson (2018) <doi:10.1109/TVCG.2017.2744685>, and the distances of distances of Lee and Jeon (2025) <doi:10.48550/arXiv.2511.02199>.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
NeedsCompilation: no
Packaged: 2026-06-29 07:05:41 UTC; mtsag
Repository: CRAN
Date/Publication: 2026-07-04 08:10:02 UTC

Detection of Outliers in High Dimensional Data

Description

Algorithms to detect high-dimensional outliers. The minimum diagonal product (MDP) of Ro, Zou, Wang and Yin (2015), the algorithm of Wilkinson that relies on nearest neighbours, and the distances of distances (DOD of Lee and Jeon (2025).

Details

Package: outliersHD
Type: Package
Version: 1.0
Date: 2026-06-29

Maintainers

Michail Tsagris <mtsagris@uoc.gr>.

Author(s)

Michail Tsagris mtsagris@uoc.gr

References

Ro K., Zou C., Wang Z. and Yin G. (2015). Outlier detection for high-dimensional data. Biometrika, 102(3): 589–599.

Wilkinson L. (2018). Visualizing big data outliers through distributed aggregation. IEEE Transactions on Visualization and Computer Graphics 24(1): 256–266.

Tsagris M., Papadakis M., Alenazi A. and Alzeley O. (2024). Computationally Efficient Outlier Detection for High-Dimensional Data Using the MDP Algorithm. Computation, 12(9): 185.

Seong-ho Lee and Yongho Jeon (2025). DOD: Detection of outliers in high dimensional data with distance of distances. https://arxiv.org/abs/2511.02199

Detection of high dimensional outliers using nearest neighbours

Description

Detection of high dimensional outliers using nearest neighbours.

Usage

ahd(x, a = 0.01, k = 10, p = 0.5, tn = 50)

Arguments

x

A matrix with numerical data with more columns (p) than rows (n), i.e. n<p.

a

Threshold for determining the cutoff for outliers. Observations are considered outliers if they fall in the (1-a) tail of the distribution of the nearest neighbor distances between exemplars.

k

The number of nearest neighbours to consider.

p

The proportion of possible outliers.

tn

Sample size to calculate an empirical threshold.

Details

For more information see Wilkinson (2018) and the R package "stray" that has implemented the algortihm. Our implementation is a faster (and slightly different) version of theirs.

Value

A list including:

scores

The score values of each observation.

outliers

The indices of the possible outlier(s).

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

References

Wilkinson L. (2018). Visualizing big data outliers through distributed aggregation. IEEE Transactions on Visualization and Computer Graphics 24(1): 256–266.

See Also

dod, rmdp

Examples

x <- matrix(rnorm(20 * 50), ncol = 50)
x <- rbind(x, matrix(rnorm(2 * 50, 5, 1), ncol = 50) )
a <- ahd(x)

Detection of high dimensional outliers using DOD

Description

Detection of high dimensional outliers using DOD.

Usage

dod(x, co = 0.1, a = 0.1)

Arguments

x

A matrix with numerical data with more columns (p) than rows (n), i.e. n<p.

co

This is to compute the c parameter (c=co\sqrt{pn}). In the paper co=0.1, and this is the default value in the function as well.

a

The parameter (a>0 and a<0.5) that represents the maximum proportion of outliers. It serves as a tuning parameter controling the maximum false positive rate.

Details

High dimensional outliers (n<<p) are detected using distances of distances.

Value

A vector with the index of the detected outlier(s).

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

References

Seong-ho Lee and Yongho Jeon (2025). DOD: Detection of outliers in high dimensional data with distance of distances. https://arxiv.org/abs/2511.02199

See Also

rmdp, ahd

Examples

x <- matrix(rnorm(20 * 50), ncol = 50)
x <- rbind(x, matrix(rnorm(2 * 50, 5, 1), ncol = 50) )
a <- dod(x)

Detection of high dimensional outliers using the RMDP

Description

Detection of high dimensional outliers using the RMDP.

Usage

rmdp(x, alpha = 0.05, itertime = 100, parallel = FALSE)

Arguments

x

A matrix with numerical data with more columns (p) than rows (n), i.e. n<p.

alpha

The significance level, i.e. used to decide whether an observation is said to be considered a possible outlier. The default value is 0.05.

itertime

The number of iterations the algorithm will be ran. The higher the sample size, the larger this number must be. With 50 observations in R^1000 maybe this has to be 1000 in order to produce stable results.

parallel

A logical value for parallel version.

Details

High dimensional outliers (n<<p) are detected using a properly constructed MCD. The variances of the variables are used and the determinant is simply their product.

Value

A list including:

runtime

The duration of the process.

dis

The final estimated Mahalanobis type normalised distances.

wei

A bollean variable vector specifying whether an observation is "clean" (TRUE) or a possible outlier (FALSE).

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

References

Ro K., Zou C., Wang Z. and Yin G. (2015). Outlier detection for high-dimensional data. Biometrika, 102(3): 589–599.

Tsagris M., Papadakis M., Alenazi A. and Alzeley O. (2024). Computationally Efficient Outlier Detection for High-Dimensional Data Using the MDP Algorithm. Computation, 12(9): 185.

See Also

dod, ahd

Examples

x <- matrix(rnorm(20 * 50), ncol = 50)
x <- rbind(x, matrix(rnorm(2 * 50, 5, 1), ncol = 50) )
a <- rmdp(x, itertime = 5)