swatanomaly

Various anomaly detection algorithms studied in anomaly detection project including K-L divergence: Cho et al. (2019)

Installation

devtools::install_github("ygeunkim/swatanomaly")

library(swatanomaly)

Kullback-Leibler Divergence Algorithm

This algorithm implements neighboring-window method. Using stats::density(), we first estimate each probability mass. Then we can compute K-L divergence from to by

where is the support of ().

The algorithm uses a threshold and check if . If this holds, two windows can be said that they are derived from the same gaussian distribution.

Fixed lambda algorithm

• Data: univariate series of size
• Input: window size , jump size for sliding window , threshold

Note that the number of window is

1. For to (w - 1) do
   1. if then
      1. be the pdf of -th window and be the pdf of (i + 1)-th window
      2. K-L divergence from to
      3. Set .
      4. 
   2. else
      1. be the pdf of normal and be the pdf of (i + 1)-th window
      2. K-L divergence from to
      3. Set .
2. output:

Dynamic lambda algorithm

• Data: univariate series of size
• Input: window size , jump size for sliding window , threshold increment , threshold updating constant

The threshold is initialized by

If , it is updated by

1. 
2. K-L from -st to -nd window
3. K-L from -nd to -rd window
4. For to (w - 1) do
   1. if then
      1. be the pdf of -th window and be the pdf of (i + 1)-th window
      2. K-L divergence from to
      3. 
      4. Set .
      5. 
   2. else
      1. be the pdf of normal and be the pdf of (i + 1)-th window
      2. K-L divergence from to
      3. Set .
5. output:

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References

Cho, Jinwoo, Shahroz Tariq, Sangyup Lee, Young Geun Kim, and Simon Woo. 2019. “Contextual Anomaly Detection by Correlated Probability Distributions using Kullback-Leibler Divergence.” WORKSHOP ON MINING AND LEARNING FROM TIME SERIES.