Table S4.

Success of the learned representation $𝐔$ in capturing the structure of the data, evaluated by running prior clustering algorithms on $𝐔$ instead of $𝐗$

	RCC						RCC-DR
Dataset	$k$-means++	AC-W	AP	SEC	LDMGI	GDL	$k$-means++	AC-W	AP	SEC	LDMGI	GDL
MNIST	0.879	0.879	0.647	0.866	0.863	NA	0.808	0.809	0.679	0.808	0.808	NA
Coil-100	0.958	0.963	0.956	0.937	0.932	0.919	0.959	0.960	0.956	0.930	0.942	0.916
YTF	0.800	0.814	0.840	0.737	0.638	0.455	0.803	0.817	0.879	0.726	0.689	0.464
YaleB	0.960	0.964	0.975	0.957	0.872	0.566	0.967	0.967	0.974	0.958	0.872	0.541
Reuters	0.544	0.544	0.511	0.472	0.372	0.341	0.545	0.545	0.525	0.492	0.528	0.421
RCV1	0.460	0.425	0.368	0.461	0.301	0.018	0.488	0.474	0.384	0.455	0.209	0.026
Pendigits	0.750	0.717	0.759	0.730	0.526	0.630	0.742	0.729	0.756	0.706	0.742	0.676
Shuttle	0.255	0.291	0.338	0.343	0.132	NA	0.275	0.340	0.344	0.495	0.327	NA
Mice Protein	0.584	0.543	0.641	0.465	0.312	0.335	0.538	0.539	0.630	0.434	0.376	0.261

Left: using the representation learned by RCC as input to prior clustering algorithms. Right: using the representation learned by RCC-DR. Accuracy is measured by AMI. The accuracy of prior algorithms increases substantially when a representation learned by RCC or RCC-DR is used as input instead of the original data. In each case, the maximum AMI is highlighted in bold. NA, not applicable.