Algorithm 1: MDST-AP algorithm

Input:  $X=\left\{x_1,x_2,\dots ,x_N\right\}:$ Set of objects (dataset of multidimensional attributes)  $\mathsf{\sigma }:$ Gaussian kernel parameter (in Equation (8))  M $:$ the number of cluster parameters P (in Equation (14))  Output:  C $=$ $\left\{C_1,C_2,\dots ,C_K\right\}:$ Set of clusters (X is divided into k clusters)

Let $r\left(i,j\right)=0, a\left(i,j\right)=0$    //responsibility and availability $\lambda$ = 0.5       //the damping coefficient $(0<\lambda <1)$ maxits = 1000    //maximum number of iterations Convits = 100     //continuous invariance times of clusters $X^{\prime }$= (X- X_mean)/X_std       //X is normalized to obtain a new dataset $X^{\prime }$ by Z-score //normalization method For t = 1 to M    //the M clustering results are obtained and the best clusters are determined//by using the DB index $S_{N\times N}$ = ComputeSimilarity($X^{″}$)   //similarity matrix $S_{N\times N}$ is calculated by Equation (1) and Equation (9) P = $\mathrm{ComputPreference}$($S_{N\times N}$, $\lambda$)  //preference P is optimized by Equation (14) If maxits <= 1000 and Convits <= 100 Then $r\left(i,j\right)$ and $a\left(i,j\right)$ are calculated by Equation (2) and Equation (3) else   //when clustering reaches 1000 iterations, or the cluster center continues 100 //unchanged the final clustering result is reached clusters = ComputeCluster(r + a, $X^{\prime }$)   //the cluster center is determined according to r + a DB_Index is calculated by Equation (15) End If End For