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Judge of Outlier

In the data of above figure, we can find there is outlier easily.

Characteristics of outlier are "Separated from majority", "Out of the range" and "In thin area of density".

We use thse characteristics to make the system to judge outlier.

Use "Separated from majority"

We use the idea of Hypothesis Testing. I we think as Normal Distribution and do Normalization , "Over 3 is outlier" is an example.

Use "Out of the range"

Simple approach. And it can be used for the case that statistical approach is difficult. Example is below.

Use "In thin area of density"

LOF is famous.

For Multi-Variable Case

Basic idea is same to the single case.

Use "Separated from majority"

Principal Component Analysis and MT method are method.

Use "Out of the range"

Principal Component Analysis and MT method are also used. For the complicated range, One-Class SVM is useful.

Use "In thin area of density"

LOF is also used for multi-varaiables.

Extreme Value Statistics

NEXT Judge of Abnormal Value