KDEOS {DDoutlier}

Kernel Density Estimation Outlier Score (KDEOS) algorithm with gaussian kernel

Description

Function to calculate a density estimation as an outlier score for observations, over a range of k-nearest neighbors. Suggested by Schubert, E., Zimek, A. & Kriegel, H-P. (2014)

Usage

KDEOS(dataset, k_min = 5, k_max = 10, eps = NULL)

Arguments

dataset

The dataset for which observations have an KDEOS score returned

k_min

The k parameter starting the k-range

k_max

The k parameter ending the k-range. Has to be smaller than the number of observations in dataset and greater than or equal to k_min

eps

An optional minimum bandwidth. If eps is smaller than the mean reachability distance for observations, eps is used. Otherwise mean reachability distance is used as bandwidth

Details

KDEOS computes a kernel density estimation over a user-given range of k-nearest neighbors. The score is normalized between 0 and 1, such that observation with 1 has the lowest density estimation and greatest outlierness. A gaussian kernel is used for estimation with a bandwidth being the reachability distance for neighboring observations. If a lower user-given bandwidth is desired, putting more weight on outlying observations, eps has to be lower than the mean reachability distance for observations. A kd-tree is used for kNN computation, using the kNN() function from the 'dbscan' package. The KDEOS function is useful for outlier detection in clustering and other multidimensional domains

Value

A vector of KDEOS scores normalized between 1 and 0, with 1 being the greatest outlierness

Author(s)

Jacob H. Madsen

References

Schubert, E., Zimek, A. & Kriegel, H-P. (2014). Generalized Outlier Detection with Flexible Kernel Density Estimates. Proceedings of the 2014 SIAM International Conference on Data Mining. Philadelphia, USA. pp. 542-550. DOI: 10.1137/1.9781611973440.63

Examples

# Create dataset
X <- iris[,1:4]

# Find outliers by setting an optional range of k's
outlier_score <- KDEOS(dataset=X, k_min=10, k_max=15)

# Sort and find index for most outlying observations
names(outlier_score) <- 1:nrow(X)
sort(outlier_score, decreasing = TRUE)

# Inspect the distribution of outlier scores
hist(outlier_score)