Detecting false data injection attacks using outlier detection

1) Input: Training data from state estimator

$Z={\left[z^{\left(1\right)},z^{\left(2\right)},\dots ,z^{\left(1000\right)}\right]}^{\text{T}}$ ,

(Total number of the samples is set as 1000)

2) Preprocess the data set Principal Component Analysis:

dimensional feature reduction of Z from 41 to 2;

2) Parameters set for the outlier detectors:

size of samples n = 200, contamination rate = 0.1 and 0.2;

3) Fit the training data in the outlier detection estimators

Estimator.fit(Z_train)

4) Sort out the outliers with the predict function of the algorithm:

$\text{Estimator}\text{.predict}\left(\text{Z\_test}\right)$

5) Return: Predicted labels $\{\begin{array}{c}1,z^{\left(p\right)}\text{isnormal}\\ -1,z^{\left(p\right)}\text{isabnormal}\end{array}$ ,

$z^{\left(p\right)}$ is some data point in the measurement data set