Algorithm 1. Simple version of the novel density-based algorithm. The steps for the novel density-based algorithm.

1: Input: Distance $d_{ij},i<j,i,j\in I_S$

2: Initialization: Cutoff distance $d_c=d_{\left[\frac{1}{2}{N}_1\left(N_1-1\right)t+\frac{1}{2}\right]}$, where [] represent rounding function and $0.1\le t\le 0.2$. Attribute of points $n_i=0,i\in I_S$.

3: Results: Number of categories of the HRRPs and the type of each sample.

4: Begin

5: Step 1. The computation of ${\left\{{\rho }_i\right\}}_{i=1}^{N_1}$ and ${\left\{q_i\right\}}_{i=1}^{N_1}$.

6: Step 2. Calculation of distance and attribute ${\left\{n_i\right\}}_{i=1}^{N_1}$.

7: Step 3. Identification of clustering centers and classification of the other points.

8: Step 4. The selection of average local density in the border region.

9: Step 5. Classification of points with the label of cluster core or cluster halo.

10: End