Nonnegative Matrix Factorization-Based Spatial-Temporal Clustering for Multiple Sensor Data Streams

Algorithm 1

STClu.

Input: Matrices 𝑋^(𝑡), 𝑋^(𝑡−1), 𝑋^{(𝑡−1,𝑡)}, 𝑅^(𝑡−1), and 𝑈^(𝑡−1), cluster number 𝑘^(𝑡), and maximum iteration 𝑇

Output: Matrices 𝐶^(𝑡), 𝑈^(𝑡), 𝑅^(𝑡), and 𝑈^{(𝑡−1,𝑡)}

(1)   use the family of Colibri methods to get 𝐶^(𝑡)

(2)  determine cluster number 𝑘^(𝑡)

(3)  initialize 𝑈^(𝑡), 𝑅^(𝑡), and 𝑈^{(𝑡−1,𝑡)} using 𝑅^(𝑡−1), 𝑈^(𝑡−1), and 𝑈^{(𝑡−1,𝑡)}, respectively

(4)  if we need to form a new partition

(5)    go to (8)

(6)  else

(7)    let 𝑅^(𝑡)=𝑅^(𝑡−1) and 𝑈^(𝑡)=𝑈^(𝑡−1), and return

(8)  while not converging and 𝑡≤𝑇 do

(9)    update 𝑈^(𝑡) by (9)

(10)     update 𝐶^(𝑡) by (10)

(11)   update 𝑅^(𝑡) by (11)

(12)     update 𝑈^{(𝑡−1,𝑡)} by (12)

(13) end while

(14) return 𝑈^(𝑡), 𝐶^(𝑡), 𝑅^(𝑡), and 𝑈^{(𝑡−1,𝑡)}