Identifying Patients with Poststroke Mild Cognitive Impairment by Pattern Recognition of Working Memory Load-Related ERP

Algorithm 1

ICA-OEMD.

Step  1. Initialize control parameters and 𝑊₀;

Step  2. Center data;

Step  3. Compute SVD of the centered data matrix;

Step  4. Estimate the kurtosis, ▵𝑊∝[𝐼−𝐾𝑡𝑎𝑛ℎ(𝑢(𝑡))𝑢^𝑇(𝑡)−𝑢(𝑡)𝑢^𝑇(𝑡)]W,

    𝑊(𝑚+1)=𝑊(𝑚)+𝜇▵𝑊(𝑚);

Step  5. Repeat Step  4 with smaller step size 𝜇 until the optimal demixing matrix 𝑊 and the source

   signals 𝑓(𝑡) are achieved;

Step  6. Initialize the residual 𝑟₁(𝑡)=𝑓(𝑡) (𝑓(𝑡) is one IC) and the index number of IMF 𝑗=1;

Step  7. Extract the jth IMF:

   (a) initialize ℎ_𝑗0(𝑡)=𝑟_𝑗(𝑡), 𝑖=0;

   (b) extract local minima and maxima of ℎ_𝑗𝑖(𝑡);

   (c) compute upper and lower envelope 𝑢_𝑗𝑖(𝑡) and 𝑣_𝑗𝑖(𝑡) by interpolating local maxima and

       local minima of ℎ_𝑗𝑖(𝑡), respectively;

   (d) compute the median 𝑚_𝑗𝑖(𝑡)=(1/2)𝑢_𝑗𝑖(𝑡)+𝑣_𝑗𝑖(𝑡);

   (e) update ℎ_𝑗𝑖+1(𝑡)=ℎ_𝑗𝑖(𝑡)−𝑚_𝑗𝑖(𝑡), 𝑖=𝑖+1;

   (f) calculate the stopping criterion according to SD=|𝑢_max+𝑣_min|/|𝑢_max−𝑣_min| until SD<𝜃₁ for some

           prescribed fraction (1−𝛼) of the total duration, while SD<𝜃₂ for the remaining fraction

           (𝛼=0.05,𝜃₁=0.05,𝜃₂=0.5);

   (g) repeat steps (b)–(f) until the stopping criterion is met, 𝑔_𝑜𝑗(𝑡)=ℎ_𝑗𝑖(𝑡) 𝑔₁(𝑡)=𝑔_𝑜1(𝑡),

    𝑔_𝑗(𝑡)=𝑔_𝑜𝑗(𝑡)−∑^𝑗−1_𝑙=1𝛽_𝑗𝑙𝑔_𝑙(𝑡), 𝑗=2,3,…,𝑛,

    ∫^𝑇₀𝑔_𝑗(𝑡)𝑔_𝑘(𝑡)=∫^𝑇₀𝑔_𝑜𝑗(𝑡)𝑔_𝑘(𝑡)−∑^𝑗−1_𝑙=1𝛽_𝑗𝑙∫^𝑇₀𝑔_𝑙(𝑡)𝑔_𝑘(𝑡)=0,  𝑘≤𝑗−1,

    ∫^𝑇₀𝑔_𝑙(𝑡)𝑔_𝑘(𝑡)𝛽=0𝑙≠𝑘,_𝑗𝑙=∫^𝑇₀𝑔_𝑜𝑗(𝑡)𝑔_𝑙(𝑡)∫^𝑇₀𝑔_𝑙²(𝑡)𝑙=𝑘, definethe𝑗thIMF𝑔_𝑗(𝑡);

Step  8. Update residual 𝑟_𝑗+1(𝑡)=𝑟_𝑗(𝑡)−𝑔_𝑗(𝑡);

Step  9. Repeat Step  7-8 with 𝑗=𝑗+1 until the expected index number of IMF is met.