Algorithm 1 Evolutionary algorithm for dimensionality reduction

1:Input: Population size P, generations G, mutation rate $\mu$, crossover rate $\rho$, fitness function S 2:Output: Optimized transformation matrix ${\mathbf{W}}^{*}$ 3:Step 1: Initialization 4:Generate an initial population of transformation matrices: $\{{\mathbf{W}}_1,{\mathbf{W}}_2,\dots ,{\mathbf{W}}_P\}$ 5:for$g=1$ to G do 6:   Step 2: Fitness Evaluation 7:   for each candidate ${\mathbf{W}}_i$ in the population do 8:          Compute fitness: $S\left({\mathbf{W}}_i\right)$ (e.g., silhouette score) 9:   end for 10: Step 3: Selection 11: Retain the top-performing candidates based on fitness 12:    Step 4: Crossover 13:    for each pair of parents ${\mathbf{W}}_{{\mathrm{parent}}_1},{\mathbf{W}}_{{\mathrm{parent}}_2}$ do 14:        if random() $<\rho$ then 15:             Generate offspring: $${\mathbf{W}}_{\mathrm{child}}={\displaystyle \frac{{\mathbf{W}}_{{\mathrm{parent}}_1}+{\mathbf{W}}_{{\mathrm{parent}}_2}}{2}}$$ 16:        end if 17:    end for 18:    Step 5: Mutation 19:    for each offspring ${\mathbf{W}}_{\mathrm{child}}$ do 20:        if random() $<\mu$ then 21:            Introduce random perturbation: $${\mathbf{W}}_{\mathrm{mutated}}={\mathbf{W}}_{\mathrm{child}}+ϵ,ϵ\sim \mathcal{N}(0,{\sigma }^2)$$ 22:        end if 23:    end for 24:    Step 6: Replacement 25:    Replace the worst-performing candidates in the population with offspring 26:end for 27:Return: Best-performing transformation matrix ${\mathbf{W}}^{*}$ based on fitness S