Algorithm 1 Landmark-based Spectral Clustering

Input: Training samples $X=\left[x_1,x_2,...,x_N\right]$, clustering number M Output: M clusters, clusters centers $C{P}_1$,$C{P}_2$,...,$C{P}_M$ 1: Produce P landmark samples using random selection or k-means methods; 2: Construct a sparse affinity matrix Z between training data samples and landmarks, with the affinity matrix calculated based on Equation (1); 3: Calculate the first M eigenvectors of $W{W}^T$, denoted by $U=\left[u_1,u_2,...,u_M\right]$; 4: Calculate $V=\left[v_1,v_2,...,v_M\right]$ based on Equation (5); 5: Each row of V is a sample and k-means is adopted to achieve the clusters and cluster centers.