New Fuzzy Support Vector Machine for the Class Imbalance Problem in Medical Datasets Classification

Algorithm 2

Kernel FSVM-CIP.

Input:

training samples {(𝐱_𝑖,𝑦_𝑖),𝑖=1,…,𝑁}

Testing samples {𝐱_𝑗,𝑗=1,…,𝑈}

Output:

The predicted labels 𝑦_𝑗 of data {𝐱_𝑗,𝑗=1,…,𝑈}

Procedure:

(1) Choose a kernel function 𝐊. Compute the Gram matrix 𝐾_𝑖𝑗=𝐾(𝐱_𝑖,𝐱_𝑗).

(2) Compute fuzzy membership 𝜇^𝜙_𝑖 using (31) or (32) for the data {(𝐱_𝑖,𝑦_𝑖),𝑖=1,…,𝑁}

(3) Construct data adjacency graph 𝐺 using 𝑘 nearest neighbors and compute the edge weights matrix 𝑊^𝜙_𝑖𝑗 with 𝑁 examples

(4) Construct local within-class preserving scatter matrix 𝐒^𝜙_lw using (24)

(5) Choose parameters 𝑡 (25); 𝜂,𝜈,𝜈₁ and 𝜈₂ (26)

(6) Compute 𝛼^∗ using (27) and 𝑏^∗ using (28) with a QP Solver

(7) Using decision function (30) with samples 𝐱_𝑗, and output the final class labels