Algorithm 1 Pseudocode for Stage 2 CCL Optimization

Require: A batch of features $\mathcal{F}$, fixed centroids $\mathcal{C}$, margin m.   1:// Step 1: Assign pseudo-labels   2:for all feature $f_i\in \mathcal{F}$do   3:      Assign pseudo-label $y_i\leftarrow arg{min}_k{\parallel f_i-C_k\parallel }_2$.   4:end for   5:// Step 2: Construct pairs and compute loss   6:Normalize features $\mathcal{F}$ to get ${\mathcal{F}}_{norm}$.   7:Compute similarity matrix $S\leftarrow {\mathcal{F}}_{norm}·{\mathcal{F}}_{norm}^{\top }$.   8:Construct positive pair set $P\leftarrow \{(i,j)\mid y_i=y_j,i<j\}$.   9:Construct negative pair set $N\leftarrow \{(i,j)\mid y_i\ne y_j,i<j\}$. 10:${\mathcal{L}}_{pos}\leftarrow {\displaystyle \frac{1}{\left|P\right|}}{\sum }_{(i,j)\in P}(1-S_{ij})$. 11:${\mathcal{L}}_{neg}\leftarrow {\displaystyle \frac{1}{\left|N\right|}}{\sum }_{(i,j)\in N}max(0,S_{ij}-m)$. 12:${\mathcal{L}}_{con}\leftarrow {\mathcal{L}}_{pos}+{\mathcal{L}}_{neg}$. 13:// Step 3: Update model 14:Update feature extractor via gradient descent on ${\mathcal{L}}_{con}$.