Algorithm 1. ASC with GNG.

Input: Data points X ∈ Rd, the number of clusters k

Output: A partition of given data points into k clusters C1,…,Ck

1: {Abstraction Level1}

2: Generate the network from the dataset X using GNG.

3: Calculate the similarity matrix A ∈ RM × M from the reference vectors and the topology of the network.

4: {Abstraction Level 2}

5: Calculate the normalized Laplacian matrix Lsym by Eq. (2).

6: Calculate the k first eigenvectors u1,…,uk of Lsym.

7: Let U ∈ RM× k be the matrix containing the vectors u1,…,uk as columns.

8: For i = 1,…, M, let yi ∈ Rk be the vector corresponding to the i-th row of U.

9: Assign (yi)i = 1,…,M to clusters C1,…,Ck by k-means.

10: {Assign data points to the clusters.}

11: Find the nearest unit to each data point.

12: Each data point is assigned to the cluster to which the nearest unit is assigned.