Details

Given a set X of n feature vectors x ₁= (x ₁₁,…,x _1p), ..., x _n= (x _n1,…,x _np) of dimension p, the problem is to identify the vectors that do not belong to the underlying distribution (see [Ben05] for exact definitions of an outlier).

The algorithm for univariate outlier detection considers each feature independently. The univariate outlier detection method can be parametric, assumes a known underlying distribution for the data set, and defines an outlier region such that if an observation belongs to the region, it is marked as an outlier. Definition of the outlier region is connected to the assumed underlying data distribution. The following is an example of an outlier region for the univariate outlier detection:

where m _n and σ _n are (robust) estimates of the mean and standard deviation computed for a given data set, α _n is the confidence coefficient, and g (n, α _n) defines the limits of the region and should be adjusted to the number of observations.