## 4 Experimental Study
### Results and Analyses
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Datasets** & **Methods** & **ACC** & **NMI** & **Purity** & **F** & **ARI** \\ \hline \multirow{8}{*}{\(1\)} & HFLRSC & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\  & NCut & 88.20 & 94.31 & 90.17 & 88.11 & 87.01 \\  & K-means & 73.94 & 85.24 & 76.54 & 73.46 & 70.79 \\  & LRR & 97.97 & 99.16 & 98.50 & 98.11 & 97.95 \\  & SSC & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\  & SC-SRGF & 92.22 & 96.58 & 94.02 & 92.54 & 91.89 \\  & USENC & **100.00** & **100.00** & **100.00** & **100.00** \\ \hline \multirow{8}{*}{\(2\)} & HFLRSC & **98.33** & **97.75** & **98.33** & **96.49** & **96.20** \\  & NCut & 87.03 & 93.32 & 89.50 & 86.69 & 85.49 \\  & K-means & 68.03 & 79.23 & 70.63 & 64.85 & 61.20 \\  & LRR & 97.42 & 98.98 & 98.17 & 97.65 & 97.45 \\  & SSC & 93.33 & 92.33 & 93.33 & 86.47 & 85.34 \\  & SC-SRGF & 88.33 & 95.35 & 91.67 & 89.27 & 88.33 \\  & USENC & 93.13 & 95.95 & 93.88 & 92.33 & 91.64 \\ \hline \multirow{8}{*}{\(3\)} & HFLRSC & **93.40** & **91.37** & **93.40** & **86.47** & **85.36** \\  & NCut & 43.05 & 47.87 & 44.77 & 28.59 & 22.31 \\  & K-means & 36.75 & 41.23 & 38.78 & 26.42 & 18.13 \\  & LRR & 80.81 & 79.46 & 81.13 & 66.37 & 63.50 \\  & SSC & 73.50 & 67.50 & 73.92 & 48.18 & 43.20 \\  & SC-SRGF & 64.15 & 63.65 & 65.97 & 46.61 & 42.06 \\  & USENC & 49.17 & 53.75 & 50.58 & 35.59 & 29.90 \\ \hline \multirow{8}{*}{\(4\)} & HFLRSC & **92.62** & **90.72** & **92.62** & **83.74** & **82.37** \\  & NCut & 23.42 & 25.77 & 24.60 & 12.17 & 2.75 \\  & K-means & 20.46 & 19.53 & 21.45 & 11.62 & 0.00 \\  & LRR & 37.12 & 38.93 & 38.85 & 19.50 & 12.31 \\  & SSC & 27.17 & 32.20 & 28.83 & 13.44 & 5.53 \\  & SC-SRGF & 38.90 & 39.82 & 40.83 & 22.05 & 15.26 \\  & USENC & 26.46 & 28.86 & 27.58 & 14.47 & 5.43 \\ \hline \multirow{8}{*}{\(5\)} & HFLRSC & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\  & NCut & 90.92 & 95.91 & 92.67 & 91.37 & 90.59 \\  & K-means & 71.10 & 82.77 & 73.69 & 69.34 & 66.18 \\  & LRR & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\  & SSC & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\  & SC-SRGF & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\  & USENC & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\ \hline \multirow{8}{*}{\(6\)} & HFLRSC & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\  & NCut & 88.65 & 94.13 & 90.45 & 88.40 & 87.35 \\  & K-means & 68.06 & 78.75 & 70.55 & 64.68 & 61.15 \\  & LRR & 95.67 & 98.23 & 96.83 & 96.01 & 95.66 \\  & SSC & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\  & SSC-SRGF & 94.72 & 94.92 & 95.02 & 91.77 & 91.08 \\  & USENC & 96.63 & 98.22 & 97.04 & 96.40 & 96.08 \\ \hline \multirow{8}{*}{\(7\)} & HFLRSC & **100.00** & **100.00** & **100.00** & **100.00** & **100.00** \\  & NCut & 78.98 & 86.87 & 81.40 & 76.16 & 74.02 \\  & K-means & 59.77 & 64.94 & 62.67 & 49.17 & 44.34 \\  & LRR & 92.08 & 95.83 & 93.70 & 91.57 & 90.83 \\  & SSC & 96.58 & 96.41 & 96.58 & 93.40 & 92.86 \\  & SC-SRGF & 90.42 & 92.94 & 91.55 & 87.14 & 86.05 \\  & USENC & 90.29 & 93.79 & 91.25 & 88.48 & 87.48 \\ \hline \end{tabular}
\end{table} 
Table 2: The clustering performances of the proposed approach and the comparison methods for the simulated datasets (1–6). The bold denotes the best results. It should be noted that when extracting the HFTC, the experimental images needed to be filtered with a Butterworth filter, which has two hyperparameters: filter order and cut-off frequency. Therefore, we designed a group of face images through a Butterworth filter to intuitively express the impact of these two production parameters on the images in Figure 4. Although we fully grasped the physical meanings of these two hyperparameters, different datasets often need different combinations of two parameters, which still need the guidance of human prior knowledge. Therefore, it would lead to great progress to propose a filter to automatically find parameters.