LOCI {DDoutlier}

Local Correlation Integral (LOCI) algorithm with constant nearest neighbor parameter

Description

Function to calculate Local Correlation Integral (LOCI) as an outlier score for observations. Suggested by Papadimitriou, S., Gibbons, P. B., & Faloutsos, C. (2003). Uses a k number of nearest neighbors instead of a constant radius

Usage

LOCI(dataset, alpha = 0.5, nn = 20, k = 3)

Arguments

dataset

The dataset for which observations have a LOCI returned

alpha

The parameter setting the size of the sampling neighborhood, as a proportion of the counting neighborhood, for observations to identify other observations in their respective neighborhood. An alpha of 1 equals a sampling neighborhood the size of the counting neighborhood (the size of distance to nn). An alpha of 0.5 equals a sampling neighborhood half the size of the counting neighborhood

nn

The number of nearest neighbors to compare sampling neighborhood with. Original paper suggest a constant user-given radius that includes at least 20 neighbors in order to introduce statistical errors in MDEF. Default is 20

k

The number of standard deviations the sampling neighborhood of an observation should differ from the sampling neighborhood of neighboring observations, to be an outlier. Default is set to 3 as used in original papers experiments

Details

LOCI computes a counting neighborhood to the nn nearest observations, where the radius is equal to the outermost observation. Within the counting neighborhood each observation has a sampling neighborhood of which the size is determined by the alpha input parameter. LOCI returns an outlier score based on the standard deviation of the sampling neighborhood, called the multi-granularity deviation factor (MDEF). The LOCI function is useful for outlier detection in clustering and other multidimensional domains

Value

npar_pi

A vector of the number of observations within the sample neighborhood for observations

avg_npar

A vector of average number of observations within the sample neighborhood for neighboring observations

sd_npar

A vector of standard deviations for observations sample neighborhood

MDEF

A vector of the multi-granularity deviation factor (MDEF) for observations. The greater the MDEF, the greater the outlierness

norm_MDEF

A vector of normalized MDEF-values, being sd_npar/avg_npar

class

Classification of observations as inliers/outliers following the rule of k

Author(s)

Jacob H. Madsen

References

Papadimitriou, S., Gibbons, P. B., & Faloutsos, C. (2003). LOCI: Fast Outlier Detection Using the Local Correlation Integral. In International Conference on Data Engineering. pp. 315-326. DOI: 10.1109/ICDE.2003.1260802

Examples

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

# Classify observations
cls_observations <- LOCI(dataset=X, alpha=0.5, nn=20, k=1)$class

# Remove outliers from dataset
X <- X[cls_observations=='Inlier',]