# VSFCM: A Novel Viewpoint-Driven Subspace Fuzzy C-Means Algorithm
## 4 Experimental Results
### UCI Data Sets  
The UCI data sets adopted here include Iris, Wireless Localization, Wine, Seeds, breast cancer Wisconsin, letter recognition (A, B), SPECT heart data, Aggregation, and Zoo. Among them, Breast Cancer data is a common medical data set in machine learning, which can be divided into two clusters. Figure 6 shows its Sammon mapping, where the yellow and purple point sets represent two classes of the dataset respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Datasets** & **Algorithms** & **CH(+)** & **NMI(+)** & **EARI(+)** & **CR(+)** & **XB(\(-\))** \\ \hline \multirow{6}{*}{DATA1} & V-FCM & 26.1104 & 0.8529 & 0.8959 & 0.9400 & 0.3092 \\  & DVPFCM & 26.2273 & 0.8997 & 0.9517 & 0.9667 & 0.2579 \\  & SCAD1 & 27.1581 & 0.9488 & 0.9795 & 0.9867 & 0.1760 \\  & ESSC & 27.1549 & 0.9702 & 0.9954 & 0.9800 & 0.1716 \\  & FRFCM & 27.1592 & **0.9830** & 0.9944 & 0.9933 & 0.1739 \\  & VSFCM & **27.1597** & **0.9830** & **0.9957** & **0.9967** & **0.1663** \\ \hline \multirow{6}{*}{DATA2} & V-FCM & 12.7069 & 0.7933 & 0.7735 & 0.8333 & 0.4738 \\  & DVPFCM & 12.9600 & 0.9264 & 0.8037 & 0.8333 & 0.4636 \\ \cline{1-1}  & SCAD1 & 13.6113 & 0.9368 & 0.9484 & 0.9667 & 0.3002 \\ \cline{1-1}  & ESSC & 14.1086 & 0.9222 & 0.9714 & 0.9778 & 0.3000 \\ \cline{1-1}  & FRFCM & 14.1692 & 0.9368 & 0.9793 & 0.9833 & 0.3330 \\ \cline{1-1}  & VSFCM & **14.2811** & **0.9534** & **0.9858** & **0.9889** & **0.2881** \\ \hline \end{tabular}  
* The bold represents the best value among all algorithms, and the underlined represents the second best.  
\end{table} 
Table 4: Clustering results on two artificial data sets. \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithms** & **Clusters** & **Weight of the Detected Three Features in Each Cluster** \\ \hline \multirow{3}{*}{VSFCM} & Cluster1 & 0.4394 & 0.2980 & 0.2626 \\  & Cluster2 & 0.3645 & 0.3285 & 0.3068 \\  & Cluster3 & 0.4380 & 0.2089 & 0.3531 \\ \hline \multirow{3}{*}{ESSC} & FRFCM & 0.3860 & 0.1960 & 0.4180 \\ \cline{1-1}  & Cluster1 & 0.3433 & 0.3321 & 0.3246 \\ \cline{1-1}  & Cluster2 & 0.3896 & 0.2573 & 0.3532 \\ \cline{1-1}  & Cluster3 & 0.3299 & 0.3400 & 0.3301 \\ \hline \multirow{3}{*}{SCAD1} & Cluster1 & 0.3284 & 0.3417 & 0.3299 \\ \cline{1-1}  & Cluster2 & 0.3500 & 0.3096 & 0.3404 \\ \cline{1-1}  & Cluster3 & 0.3393 & 0.3327 & 0.3280 \\ \hline \end{tabular}  
* From Table 3, we can find that the weight of the ESSC and SCAD1 algorithm does not fluctuate very much around 0.3333, but our VSFCM algorithm has a large difference in the attribution of weights. Taking Cluster 1 as an example, three weights, 0.3433, 0.3321, and 0.3246 of ESSC, are very close. However, the weight values obtained by the VSFCM algorithm are 0.4394, 0.2980, and 0.2626. From the VSFCM algorithm, it can be seen that the first feature has a significant contribution to the clustering result, followed by the second feature, and the worst is the third feature.  
\end{table} 
Table 3: Dimensional weight distribution of algorithms on DATA2. Figure 7 shows the \(\rho-\delta\) distribution diagram of Breast Cancer of two cluster center initialization methods. In Figure 7, we can see that the first initial cluster center is well determined, that is, the data point in the upper right corner. In the selection process of the second initial cluster center, the boundary between the optional points of the CDCI algorithm and other data points is very clear, while that of the HDCCI algorithm is fuzzy. So, when we use the HDCCI algorithm to select the initial cluster center, it is easy to choose the wrong one. In contrast, the initial cluster centers selected by our cluster center initialization method CDCI are more in line with the characteristics of the ideal cluster centers. Table 5 describes the average value of the results of each clustering algorithm (including V-FCM, SCAD, ESSC, FRPCM, DVPFCM, and our algorithm) running 20 times on the selected UCI data sets. The adopted evaluation indicators here are the above-mentioned three hard indicators (CR, CH, and NMI) and two fuzzy indicators (EARI and XB).