Table 2. Clustering performance.

For each data set, bold highlights the method with the best performance on each measure between each group of algorithms (SNE, LLE or ISOMAP based). The overall superior method for each data set is depicted with an asterisk (*). The parameters $Perp$ and NN refer to the selected perplexity and number of nearest neighbours, respectively. They were optimised for the corresponding methods. Due to the non-convexity of SNE-based approaches, the mean (and standard deviation) of $100$ separate runs on the same data is reported.

Data Set	Algorithm	Accuracy	NMI	RI	ARI
Handwritten digits	$\mathrm{S}\mathrm{N}{\mathrm{E}}_{concat}$ (Perp = 10)	0.717 (0.032)	0.663 (0.013)	0.838 (0.005)	0.568 (0.026)
	m-SNE (Perp = 10)	0.776 (0.019)	0.763 (0.009)	0.938 (0.004)	0.669 (0.019)
	multi-SNE* (Perp = 10)	0.882 (0.008)	0.900 (0.005)	0.969 (0.002)	0.823 (0.008)
	$\mathrm{L}\mathrm{L}{\mathrm{E}}_{concat}$ (NN = 10)	0.562	0.560	0.871	0.441
	m-LLE (NN = 10)	0.632	0.612	0.896	0.503
	multi-LLE (NN = 5)	0.614	0.645	0.897	0.524
	$\mathrm{I}\mathrm{S}\mathrm{O}\mathrm{M}\mathrm{A}{\mathrm{P}}_{concat}$ (NN = 20)	0.634	0.619	0.905	0.502
	m-ISOMAP (NN = 20)	0.636	0.628	0.898	0.477
	multi-ISOMAP (NN = 5)	0.658	0.631	0.909	0.518
Caltech7	$\mathrm{S}\mathrm{N}{\mathrm{E}}_{concat}$ (Perp = 50)	0.470 (0.065)	0.323 (0.011)	0.698 (0.013)	0.290 (0.034)
	m-SNE* (Perp = 10)	0.542 (0.013)	0.504 (0.029)	0.757 (0.010)	0.426 (0.023)
	multi-SNE (Perp = 80)	0.506 (0.035)	0.506 (0.006)	0.754 (0.009)	0.428 (0.022)
	$\mathrm{L}\mathrm{L}{\mathrm{E}}_{concat}$ (NN = 100)	0.425	0.372	0.707	0.305
	m-LLE (NN = 5)	0.561	0.348	0.718	0.356
	multi-LLE (NN = 80)	0.638	0.490	0.732	0.419
	$\mathrm{I}\mathrm{S}\mathrm{O}\mathrm{M}\mathrm{A}{\mathrm{P}}_{concat}$ (NN = 20)	0.408	0.167	0.634	0.151
	m-ISOMAP (NN = 5)	0.416	0.306	0.686	0.261
	multi-ISOMAP (NN = 10)	0.519	0.355	0.728	0.369
Caltech7 (balanced)	$\mathrm{S}\mathrm{N}{\mathrm{E}}_{concat}$ (Perp = 80)	0.492 (0.024)	0.326 (0.018)	0.687 (0.023)	0.325 (0.015)
	m-SNE (Perp = 10)	0.581 (0.011)	0.444 (0.013)	0.838 (0.022)	0.342 (0.016)
	multi-SNE* (Perp = 20)	0.749 (0.008)	0.686 (0.016)	0.905 (0.004)	0.619 (0.009)
	$\mathrm{L}\mathrm{L}{\mathrm{E}}_{concat}$ (NN = 20)	0.567	0.348	0.725	0.380
	m-LLE (NN = 10)	0.403	0.169	0.617	0.139
	multi-LLE (NN = 5)	0.622	0.454	0.710	0.391
	$\mathrm{I}\mathrm{S}\mathrm{O}\mathrm{M}\mathrm{A}{\mathrm{P}}_{concat}$ (NN = 5)	0.434	0.320	0.791	0.208
	m-ISOMAP (NN = 5)	0.455	0.299	0.797	0.224
	multi-ISOMAP (NN = 5)	0.548	0.368	0.810	0.267
Cancer types	$\mathrm{S}\mathrm{N}{\mathrm{E}}_{concat}$ (Perp = 10)	0.625 (0.143)	0.363 (0.184)	0.301 (0.113)	0.687 (0.169)
	m-SNE (Perp = 10)	0.923 (0.010)	0.839 (0.018)	0.876 (0.011)	0.922 (0.014)
	multi-SNE* (Perp = 20)	0.964 (0.007)	0.866 (0.023)	0.902 (0.005)	0.956 (0.008)
	$\mathrm{L}\mathrm{L}{\mathrm{E}}_{concat}$ (NN = 10)	0.502	0.122	0.091	0.576
	m-LLE (NN = 20)	0.637	0.253	0.235	0.647
	multi-LLE (NN = 10)	0.850	0.567	0.614	0.826
	$\mathrm{I}\mathrm{S}\mathrm{O}\mathrm{M}\mathrm{A}{\mathrm{P}}_{concat}$ (NN=5)	0.384	0.015	0.009	0.556
	m-ISOMAP (NN = 10)	0.390	0.020	0.013	0.558
	multi-ISOMAP (NN = 50)	0.514	0.116	0.093	0.592