Robust Missing Traffic Flow Imputation Considering Nonnegativity and Road Capacity

Algorithm 1

Matrix completion based traffic data imputation method.

Input: Observation samples 𝐷_𝑖𝑗, 𝑖,𝑗∈Ω, of matrix 𝐷∈𝑅^𝑚×𝑛

(1) 𝑌₀,𝐸₀=0,𝜇₀,𝑘=0,𝐶(roadcapacity)

(2) while not converged do

(3) (𝑈,𝑆,𝑉)=𝑠𝑣𝑑𝐷−𝐸_𝑘+𝜇_𝑘⁻¹𝑌_𝑘,

(4) 𝐴_𝑘+1=𝑈𝑆_𝜇𝑘⁻¹𝑉^𝑇,

(5) 𝐸_𝑘+1=𝑃_{𝐷−𝑐≤𝐸≤𝐷}𝑃_Ω𝑆_𝜇/𝜆𝐷−𝐴_𝑘+1+𝜇_𝑘⁻¹𝑌_𝑘+𝑃_Ω𝐷−𝐴_𝑘+1+𝜇_𝑘⁻¹𝑌_𝑘

(6) 𝑌_𝑘+1=𝑌_𝑘+𝜇_𝑘𝐷−𝐴_𝑘+1−𝐸_𝑘+1

(7) updating 𝜇_𝑘

(8) 𝑘=𝑘+1

(9) end while

(10) output 𝐴