The Outlier Interval Detection Algorithms on Astronautical Time Series Data

Pseudocode 1

Input: 𝑋 is the TSD, and 𝑐 is the count of the intervals.

Output: The top 𝐾 outlier intervals in time domain 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) 𝑎=∑_{𝑥𝑗∈𝑡𝑖}𝑥²_𝑗,𝑏=∑_{𝑥𝑗∈𝑡𝑖}𝑥_𝑗

 (4) var(𝑡_𝑖𝑎)=|𝑡_𝑖|−𝑏𝑡_𝑖²

 (5) endfor

 (6) Outlier(𝑇,𝐾)=argmax^𝐾_{𝑡𝑖∈𝑇}{var(𝑡_𝑖)}

 The time complexity of the VOID is 𝑂(𝑁) where 𝑁 is the number of data in the TSD.