# VSFCM: A Novel Viewpoint-Driven Subspace Fuzzy C-Means Algorithm
## 4 Experimental Results
### Discussion  
This study proposes a new and more effective cut-off distance, using high-density points to achieve the initialization of the cluster center and the selection of viewpoints. This can effectively restrain the interference of noise (because the ideal cluster center has a large value of the \(\rho\) and \(\delta\), but the \(\delta\) value of the noise point is small). Therefore, the cluster center initialization method CDCI in this study is better than the DPC and the HDCCI (the initialization method of DVPPCM). In addition, we test the performance of our proposed VSFCM algorithm and other algorithms on two artificial data sets, 10 UCI data sets, and the Olivetti face database. Through comparison, it is found that the proposed VSFCM algorithm performs better than V-FCM, DVPPCM, SCAD1, ESSC, and FRPCM in five indicators, and the distribution of feature weights of our algorithm is more in line with the characteristics of the data. Finally, we compare the average number of iterations and iteration time of each algorithm and discover that the number of iterations and iteration time required by the VSFCM algorithm is generally less, which leads to the conclusion that the VSFCM algorithm has a better convergence speed. From a deeper perspective, the proposed VSFCM algorithm has better performance due to the following aspects:  
* First, the proposed cluster center initialization method CDCI can get the initial cluster center close to the real data structure through the new cut-off distance. This not only prevents the iterative divergence of the algorithm but also speeds up the convergence of the algorithm and helps improve the accuracy of the algorithm;
* Second, as a part of the data structure of the VSFCM algorithm, the viewpoint serves for the knowledge-induced clustering process. Moreover, it is combined with data to form \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **V-FCM** & **DVPPCM** & **SCAD1** & **ESSC** & **FRPCM** & **VSFCM** \\ \hline D1 & 18 (3) & 51 (6) & 16 (2) & 20 (4) & 7 (1) & 20 (4) \\ D2 & 37 (5) & 121 (6) & 12 (2) & 13 (3) & 10 (1) & 19 (4) \\ D3 & 10 (2) & 26 (6) & 19 (5) & 16 (4) & 7 (1) & 15 (3) \\ D4 & 7 (2) & 22 (6) & 13 (4) & 12 (3) & 5 (1) & 16 (5) \\ D5 & 42 (4) & 104 (5) & 15 (3) & 15 (3) & 8 (1) & 12 (2) \\ D6 & 10 (2) & 56 (6) & 16 (4) & 19 (5) & 11 (3) & 9 (1) \\ D7 & 9 (2) & 20 (5) & 16 (4) & 46 (6) & 6 (1) & 12 (3) \\ Arank & 2.9 (2) & 5.7 (6) & 3.4 (4) & 4 (5) & **1.3 (1)** & 3.1 (3) \\ \hline \hline \end{tabular} The bold represents the best value among all algorithms, and the underlined represents the second best.  
\end{table} 
Table 8: Average number of iterations of each algorithm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **V-FCM** & **DVPPCM** & **SCAD1** & **ESSC** & **FRPCM** & **VSFCM** \\ \hline D1 & 0.4836 (6) & 0.1836 (5) & 0.1189 (4) & 0.0345 (1) & 0.0934 (2) & 0.1150 (3) \\ D2 & 4.7661 (5) & 11.2978 (6) & 1.0110 (3) & 0.5590 (1) & 1.2039 (4) & 0.9489 (2) \\ D3 & 0.0473 (1) & 0.1282 (5) & 0.1839 (6) & 0.0763 (2) & 0.1146 (4) & 0.0960 (3) \\ D4 & 0.3458 (2) & 0.6581 (5) & 0.6268 (4) & 0.2555 (1) & 1.0447 (6) & 0.5627 (3) \\ D5 & 0.1581 (6) & 0.0473 (1) & 0.1011 (3) & 0.0796 (2) & 0.1507 (5) & 0.1287 (4) \\ D6 & 0.1549 (1) & 0.4161 (4) & 0.5214 (5) & 0.2669 (3) & 1.6541 (6) & 0.2050 (2) \\ D7 & 2.1087 (5) & 4.2933 (6) & 1.1066 (3) & 1.3857 (4) & 1.0721 (2) & 0.6442 (1) \\ Arank & 3.7 (3) & 4.6 (6) & 4 (4) & **2 (1)** & 4.1 (5) & 2.6 (2) \\ \hline \hline \end{tabular} The bold represents the best value among all algorithms, and the underlined represents the second best.  
\end{table} 
Table 9: Average running time of each algorithm. a cluster driving force driven by both knowledge and data, inducing the clustering algorithm to obtain more accurate clustering results.