# VSFCM: A Novel Viewpoint-Driven Subspace Fuzzy C-Means Algorithm
## 4 Experimental Results
### Evaluation Indicator  
We use two types of evaluation indicators: hard clustering effectiveness indicators and soft clustering effectiveness indicators. Moreover, the superscript \"(+)\" indicates that the larger the value of the indicator, the better the clustering performance. The superscript \"(-)\" indicates the opposite meaning. Since fuzzy clustering algorithms divide data points into the clusters with the highest corresponding membership, hard clustering indicators can also be used to evaluate their clustering effects. The hard clustering effectiveness indicators selected are the following three kinds. The classification rate (CR) [32] reflects the proportion of data that are correctly classified. The formula is:  
\[\text{CR}^{(+)}=\frac{\sum\limits_{i=1}^{C}e_{i}}{n}. \tag{40}\]  
in which \(e_{i}\) is the number of objects found correctly in the \(i\)-th cluster, and \(n\) is the number of all objects in the data set. Normalized mutual information (NMI) [35] reflects the statistical information shared between two clusters:  
\[\text{NMI}^{(+)}(W,V)=\frac{\sum\limits_{i=1}^{I}\sum\limits_{j=1}^{J}q(i,j) \log\frac{q(i,j)}{q(i)q(j)}}{\sqrt{G(W)G(V)}}. \tag{41}\]  
Here \(W,V\) are the two distributions of the data set. Supposing that \(W,V\) have \(I\) and \(J\) clusters, respectively. In addition, \(q(i)=\frac{|w_{i}|}{n}\), and \(|W_{i}|\) is the number of objects contained \begin{table}
\begin{tabular}{c c c c c} \hline
**ID** & **Name** & **Instances** & **Features** & **Clusters** \\ \hline D1 & Iris & 150 & 4 & 3 \\ D2 & Wireless Indoor Localization & 2000 & 7 & 4 \\ D3 & Wine & 178 & 13 & 3 \\ D4 & Breast cancer & 569 & 30 & 2 \\ D5 & Seeds & 210 & 7 & 3 \\ D6 & Letter Recognition (A, B) & 1155 & 16 & 2 \\ D7 & Ionosphere & 351 & 33 & 2 \\ D8 & SPECT heart data & 267 & 22 & 2 \\ D9 & Aggregation & 788 & 2 & 7 \\ D10 & Zoo & 101 & 17 & 7 \\ D11 & DATA1 & 300 & 2 & 3 \\ D12 & DATA2 & 180 & 3 & 3 \\ \hline \end{tabular}
\end{table} 
Table 2: Testing data sets. in the cluster \(W_{i}\). \(q(i,j)=\frac{\left|\Psi_{i}\cap V_{j}\right|}{n}\), and \(G(W)=-\sum\limits_{i=1}^{l}q(i)\log q(i)\). The structure of the calculation formula of \(G(V)\) is similar. 3. Calinski-Harabasz indicator  
The Calinski-Harabasz (CH) indicator [36] is a measure from the perspective of distance within a cluster and dispersion between clusters:  
\[\text{CH}^{(+)}=\frac{\sum\limits_{i=1}^{c}n_{i}\times d(v_{i},\overline{v})} {c-1}\,/\frac{\sum\limits_{i=1}^{c}\sum\limits_{k=1}^{n}d(x_{k},v_{i})}{n-c}\,. \tag{42}\]  
Here \(n_{i}\) corresponds to the number of objects contained in cluster \(i\), and \(\overline{v}\) is the average of the cluster centers. The following two kinds of soft clustering effectiveness indicators are used. 1. The extension indicator of ARI  
The EARI [37] indicator is a fuzzy extension of the adjusted rand indicator (ARI) [38; 39], and its purpose is to describe the similarity of two clustering results. Assuming that R and Q are two hard partitions, corresponding to k and v clusters, respectively, there are some definitions in the ARI indicator as follows:  
\(e\) represents the number of pairs of data belonging to the same class in R and to the same cluster in Q meanwhile. \(f\) represents the number of pairs of data belonging to the same class in R and to the different clusters in Q meanwhile. \(g\) represents the number of pairs of data belonging to the different classes in R and to the same cluster in Q meanwhile. \(h\) represents the number of pairs of data belonging to the different classes in R and to the different clusters in Q meanwhile.