ALGORITHM 1.

Pipeline of the semi-supervised self-training clustering algorithm under low-rank representation

Input	X - The original data matrix;
	λ - The control parameter of LRR;
	distZ, distE - The distance metrics of K-means for clustering Z and E, respectively;
	maxIterNum - The max number of iteration.
Output	IZ - The clustering results, among which the labels of unlabeled samples are predicted.
Step 1:	Perform LRR on original data matrix X.
	$$\begin{gathered} \underset{\mathbf{Z},\mathbf{E}}{min}{\Vert \mathbf{Z}\Vert }_{\ast }+\lambda {\Vert \mathbf{E}\Vert }_{2,1} \\ s.t.,\mathbf{X}=\mathbf{XZ}+\mathbf{E}; \end{gathered}$$
	Re-arrange Z and E as $\mathbf{Z}=[\begin{array}{cc}{\mathbf{Z}}_l& {\mathbf{Z}}_u\end{array}]$ and $\mathbf{E}=[\begin{array}{cc}{\mathbf{E}}_l& {\mathbf{E}}_u\end{array}]$, respectively;
	currentIterNum ← 0; // Counter of clustering iterations
Step 2:	Perform K-means algorithm on Z and E, respectively.
	lZ = K-means(Z,distZ); //Using (1) to determine the initial point of each cluster.
	lE = K-means(E,distE); // Using a method similar to (1) to determine the initial point of each cluster
	// lZ and lE are the clustering results on Z and E, respectively;
	currentIterNum ← currentIterNum 1;
Step 3:	Select unlabeled samples as labeled ones for next round clustering.
	S ← Φ;
	FOR each unlabeled sample i in Zu
	Let lzi and lei be the predicted labels of sample i according to the clustering results of lZ and lE, respectively.
	IF lzi = lei
	S ← S ∪{i}; //select an unlabeled sample
	END IF
	END FOR
Step 4:	Decide whether to terminate the algorithm, and update Z and E.
	IF S = ø; or currentIterNum > maxIterNum:
	RETURN lZ;
	ELSE
	FOR each selected unlabeled sample i in S
	move ${\mathbf{z}}_i^u$ from Zu to Zl;
	move ${\mathbf{e}}_i^u$ from Eu to El;
	END FOR
	$\mathbf{Z}\leftarrow [\begin{array}{cc}{\mathbf{Z}}_l& {\mathbf{Z}}_u\end{array}]$; //update Z
	$\mathbf{E}\leftarrow [\begin{array}{cc}{\mathbf{E}}_l& {\mathbf{E}}_u\end{array}]$; //update E
	GOTO Step 2;
	END IF