Table 3. 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.

Data set	Algorithm	Accuracy	NMI	RI	ARI
NDS	$\mathrm{S}\mathrm{N}{\mathrm{E}}_{concat}$ (Perp = 80)	0.747 (0.210)	0.628 (0.309)	0.817 (0.324)	0.598 (0.145)
	m-SNE (Perp = 50)	0.650 (0.014)	0.748 (0.069)	0.766 (0.022	0.629 (0.020)
	multi-SNE* (Perp = 80)	0.989 (0.006)	0.951 (0.029)	0.969 (0.019)	0.987 (0.009)
	$\mathrm{L}\mathrm{L}{\mathrm{E}}_{concat}$ (NN = 5)	0.606 (0.276)	0.477 (0.357)	0.684 (0.359)	0.446 (0.218)
	m-LLE (NN = 20)	0.685 (0.115)	0.555 (0.134)	0.768 (0.151)	0.528 (0.072))
	multi-LLE (NN = 20)	0.937 (0.044)	0.768 (0.042)	0.922 (0.028)	0.823 (0.047)
	$\mathrm{I}\mathrm{S}\mathrm{O}\mathrm{M}\mathrm{A}{\mathrm{P}}_{concat}$ (NN = 100)	0.649 (0.212)	0.528 (0.265)	0.750 (0.286)	0.475 (0.133)
	m-ISOMAP (NN = 5)	0.610 (0.234)	0.453 (0.221)	0.760 (0.280)	0.386 (0.138)
	multi-ISOMAP (NN = 300)	0.778 (0.112)	0.788 (0.234)	0.867 (0.194)	0.730 (0.094)
MCS	$\mathrm{S}\mathrm{N}{\mathrm{E}}_{concat}$ (Perp = 200)	0.421 (0.200)	0.215 (0.185)	0.711 (0.219)	0.173 (0.089)
	m-SNE (Perp = 2)	0.641 (0.069)	0.670 (0.034)	0.854 (0.080)	0.575 (0.055)
	multi-SNE* (Perp = 50)	0.919 (0.046)	0.862 (0.037)	0.942 (0.052)	0.819 (0.018)
	$\mathrm{L}\mathrm{L}{\mathrm{E}}_{concat}$ (NN = 50)	0.569 (0.117)	0.533 (0.117)	0.796 (0.123)	0.432 (0.051)
	m-LLE (NN = 20)	0.540 (0.079)	0.627 (0.051)	0.819 (0.077)	0.487 (0.026)
	multi-LLE (NN = 20)	0.798 (0.059)	0.647 (0.048)	0.872 (0.064)	0.607 (0.022)
	$\mathrm{I}\mathrm{S}\mathrm{O}\mathrm{M}\mathrm{A}{\mathrm{P}}_{concat}$ (NN = 150)	0.628 (0.149)	0.636 (0.139)	0.834 (0.167)	0.526 (0.071)
	m-ISOMAP (NN = 5)	0.686 (0.113)	0.660 (0.106)	0.841 (0.119)	0.565 (0.051)
	multi-ISOMAP (NN = 300)	0.717 (0.094)	0.630 (0.101)	0.852 (0.118)	0.570 (0.044)