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

Algorithm 1

FSVM-CIP in the linear case.

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) Compute fuzzy membership 𝜇_𝑖 using (22) or (23) for the data {(𝐱_𝑖,𝑦_𝑖),𝑖=1,…,𝑁}

(2) Construct data adjacency graph 𝐺 using 𝑘 nearest neighbors and compute the edge weights matrix 𝑊_𝑖𝑗 with 𝑁 examples

(3) Construct local within-class preserving scatter matrix 𝐒_lw using (8)

(4) Choose parameters 𝑡 (6); 𝜂,𝜈,𝜈₁ and 𝜈₂ (8)

(5) Compute 𝛼^∗ using (15) and 𝑏^∗ using (17) with a QP Solver

(6) Using decision function (19) with samples 𝐱_𝑗, and output the final class labels