Algorithm 2: Proposed PCA-based subspace clustering.

Input: Data $X$, number of subspaces $k$, sampling size $n$, regularization parameter ${\lambda }_1$ and ${\lambda }_2$, neighborhood threshold $d_{\max }$, residual minimization parameter $m$, affinity threshold $t_{\max }$. Output: The label vector $l$ of all points in $X$ with clustered values.  1. The uniform sampling of $n$ points $\tilde{X}$ from $X$ is performed.  2. The subclusters are constructed.  3. Implement PCA on the subclusters.  4. An affinity matrix is constructed.  5. The adjacency matrix is sparsified.   For $j=1\begin{array}{cc}& \end{array}\begin{array}{cc}to& n\begin{array}{cc}& do\end{array}\end{array}$   $w:={\left[D\right]}_j$   For $i=1\begin{array}{cc}& to\begin{array}{cc}& n\begin{array}{cc}& do\end{array}\end{array}\end{array}$   If ${\left[D\right]}_{ij}\le w\left(n-d_{\max }\right)$, then    ${ \left|D\right|}_{ij}:=0$    End   End  6. Cluster $\tilde{X}:set\begin{array}{cc}D:=D+D^T& \end{array}$.  7. Sample points in $\tilde{X}$ are clustered by implementing spectral clustering on $D$.  8. Indicate the labels of $\tilde{X}$ by $l_{in}$.  9. The label of the entire dataset $X$ is obtained by combining $l_{in}$ and $l_{out}$ so that the entire $l$ can be obtained and the clustering is performed successfully.