Algorithm S1.

Joint Clustering and Dimensionality Reduction

I:	input: Data samples ${\{𝐱\}}_{i=1}^n$, dimensionality $d$, parameters $\gamma$, $\xi$, $\eta$.
II:	output: Cluster assignment ${\{{\widehat{c}}_i\}}_{i=1}^n$ and latent factors $𝐃$.
III:	Construct connectivity structure $\mathcal{E}$.
IV:	Initialize dictionary $𝐃$ and codes $𝐙$.
V:	Precompute $w_{p,q}$, ${\delta }_1$, ${\delta }_2$.
Vi:	Initialize ${𝐮}_i={𝐳}_i$, $l_i^{\text{𝟣}}$ $=1$, $l_{p,q}^{\text{𝟤}}$ $=1$,${\mu }_1=\xi {\delta }_1$, ${\mu }_2\gg \max {\parallel {𝐳}_p-{𝐳}_q\parallel }_2^2$, $\lambda$.
VII:	while $\left|{𝐂}^t-{𝐂}^{t-1}\right|<\epsilon$ or $t$ < maxiterations do
VIII:	Update $l_i^{\text{𝟣}}$ and $l_{p,q}^{\text{𝟤}}$ using Eq. 5.
IX:	Update ${\{{𝐳}_i\}}_{i=1}^n$ using Eq. 14.
X:	Update ${\{{𝐮}_i\}}_{i=1}^n$ using Eq. 12.
XI:	Every 4 iterations, update $\lambda$, ${\mu }_i=\max \left(\frac{{\mu }_i}{2},\frac{{\delta }_i}{2}\right)$.
XII:	Every 10 iterations, update $𝐃$ using Eq. 17.
XIII:	Construct graph $\mathcal{G}=(\mathcal{V},\mathcal{F})$ with $f_p,q=1$ if ${\parallel {𝐮}_p^{\ast }-{𝐮}_q^{\ast }\parallel }_2<{\delta }_2$.
XIV:	Output clusters given by the connected components of $\mathcal{G}$.