Algorithm 1: Pseudocode of the FCM algorithm

Set the fuzzy index $m$, iteration accuracy $\epsilon$, and maximum category number $c_{\mathrm{m}\mathrm{a}\mathrm{x}}$ for $c=1,2,\cdots ,c_{\mathrm{m}\mathrm{a}\mathrm{x}}$     $l=0$     Initialize ${\mathbf{V}}^{\left(l\right)}\in {\mathbb{R}}^{c\times g}$ and ${\mathbf{U}}^{\left(l\right)}\in {\mathbb{R}}^{c\times N}$ randomly     while True         $l=l+1$         Update ${\mathbf{U}}^{\left(l\right)}$ with Equation (20)         Update ${\mathbf{V}}^{\left(l\right)}$ with Equation (21)         if [In Equation (22) is satisfied]             break while         end if     end while     ${\mathbf{U}=\mathbf{U}}^{\left(l\right)},{\mathbf{V}=\mathbf{V}}^{\left(l\right)}$     Calculate the clustering validity function $P\left(c,\mathbf{U},\mathbf{V}\right)$ with Equation (23) end for Choose the optimal ${c(c}^{*})$ with Equation (24) return $c^{*}$ and the corresponding $\mathbf{V},\mathbf{U}$