The Outlier Interval Detection Algorithms on Astronautical Time Series Data

Pseudocode 2

Input: 𝑋 is the TSD, and 𝑐 is the count of the intervals, [𝜏₁,𝜏₂] are the amplitude thresholds.

Output: The top 𝐾 outlier intervals and their scores.

 (1) 𝑇 is the set of 𝑐 intervals divided from 𝑋, that is, 𝑇={𝑡_𝑖∣⋃^𝑐_𝑖=1𝑡_𝑖=𝑋,𝑡_𝑖∩𝑡_𝑗=𝜙(𝑖≠𝑗)}

 (2) for each 𝑡_𝑖 in 𝑇

 (3) 𝑓_𝑡𝑖=FFT(𝑡_𝑖)⊗[𝜏₁,𝜏₂],where𝑎⊗[𝜏₁,𝜏₂𝜏]=²,𝑎≥𝜏₂𝑎,𝜏₁<𝑎<𝜏₂0,𝑎≤𝜏₁

 (4) endfor

 (5) for each 𝑡_𝑖 in 𝑇

 (6) 𝑑(𝑡_𝑖)=∑_{𝑓𝑡𝑗∈𝑘𝑛𝑛(𝑓𝑡𝑖)}|𝑓_𝑡𝑖−𝑓_𝑡𝑗|²

 (7) endfor

 (8) Outlier(𝑇,𝐾)=argmax^𝐾_{𝑡𝑖∈𝑇}{𝑑(𝑡_𝑖)}