Table 1 Notations and their description
From: EPASAD: ellipsoid decision boundary based Process-Aware Stealthy Attack Detector
Notation | Description |
|---|---|
\(\mathbb {R}\) | Set of Real numbers |
\(\mathbb {I}\) | Set of Integers |
\(m_i\) | \(i\text{th}\) Measurement |
\(\textbf{M}\) | Trajectory Matrix of size \(L\times K\) |
m | \(L\)-length lagged vector |
\(M_i\) | A specific lagged vector of length L, \(i\text{th}\) column vector of \(\textbf{M}\) or test subsequence for \(i\text{th}\) measurement |
c | Centroid vector in \(\mathbb {R}^L\) |
\(\textbf{P}\) | Projection matrix |
\(\textbf{U}\) | Eigen matrix |
\(U_i\) | \(i\text{th}\) Eigenvector |
\(\textbf{X}\) | A signal subspace matrix of size \(R\times K'\) |
\(X_i\) | A specific \(R\)-length lagged vector in \(\mathbb {R}^R\), \(i\text{th}\) column vector of \(\textbf{X}\) or projected test subsequence for \(i\text{th}\) measurement |
x | A \(R\)-length lagged vector in signal subspace |
w | A weight vector in \(\mathbb {R}^R\) |
\(\hat{c}\) | Centroid vector in \(\mathbb {R}^R\) |
\(\mathcal {D}_t\) | Departure score at timestamp t |
\(\theta _p\) | Threshold of PASAD |
\(\theta _e\) | Threshold of EPASAD |
\(\delta _f(x)\) | Tightness of decision boundary f(x) at a point x |
N | Length of training subsequence |
\(N'\) | Length of training + validation subsequence |
L | Lag parameter in \(\mathbb {I}\) |
R | Dimensionality of signal subspace parameter |
\(\epsilon\) | Slack-value parameter |
\(\prod (w)\) | Product of elements of vector w |