Algorithm 1.

RCC

I: input: Data samples ${\{𝐱\}}_{i=1}^n$.

II: output: Cluster assignment ${\{{\widehat{c}}_i\}}_{i=1}^n$.

III: Construct connectivity structure $\mathcal{E}$.

IV: Precompute $\chi ={\parallel 𝐗\parallel }_2,w_{p,q},\delta$.

V: Initialize ${𝐮}_i={𝐱}_i,l_{p,q}=1,\mu \gg \max {\parallel {𝐱}_p-{𝐱}_q\parallel }_2^2,\lambda =\frac{\chi }{{\parallel 𝐀\parallel }_2}$.

VI: while $\left|{𝐂}^t-{𝐂}^{t-1}\right|<\epsilon$ or $t$ < maxiterations do

VII: Update $l_{p,q}$ using Eq. 5 and $𝐀$ using Eq. 8.

VIII: Update ${\{{𝐮}_i\}}_{i=1}^n$ using Eq. 7.

IX: Every four iterations, update $\lambda =\frac{\chi }{{\parallel 𝐀\parallel }_2}$, $\mu =\max \left(\frac{\mu }{2},\frac{\delta }{2}\right)$.

X: Construct graph $\mathcal{G}=(\mathcal{V},\mathcal{F})$ with $f_{p,q}=1$ if ${\parallel {𝐮}_p^{\ast }-{𝐮}_q^{\ast }\parallel }_2<\delta$.

XI: Output clusters given by the connected components of $\mathcal{G}$.