# Cluster-Centered Visualization Techniques for Fuzzy Clustering Results to Judge Single Clusters
## 5 Validation by Example
### Hepatitis-C-Virus Data Set  
In addition to the already-mentioned data sets, the CCV techniques are also applied to a second real data set. The HCV data set contains laboratory values of blood donors, Hepatitis C patients, and demographic values like age [33]. The target attribute contains normal blood donors vs. Hepatitis C patients, including its progress with 'just' Hepatitis C, Fibrosis, Cirrhosis. The fuzzy \(k\)-means clustering algorithm is also applied to determine the clustering results. For the visualization of the clustering results, CCV techniques are used. The following figures show the results of the visualization for the HCV data set with 2, 3, and 4 clusters. The CPC method always puts the first cluster center in the middle, all other centers on the edge, and all data points inside the circle. The A2C method always uses the first and second cluster centers for the angle-based visualization. The AM method also always uses the first cluster center for the angle-based visualization. The colors of the clusters are red for the first, black for the second, green for the third, and blue for the fourth cluster.  
Figure 11 shows the HCV data set with two clusters. With the CPC method (left), two clusters are separated, but the data points seem to merge smoothly from the red cluster to the black cluster. Therefore, a clear separation is not visible. The A2C method (middle) leads to a better visualization of the fact that the two clusters are partially separated. The AM method (right) shows the same result.  
Figure 12 shows the HCV data set with three clusters. With the CPC method (left), three clusters are separated, but some data points from the red cluster are attracted to the green and black cluster. The A2C method (middle) shows a better, more clear separation. With the AM method (right), the same result is visible.  
Figure 10: Iris data set with four clusters and visualized results with the CPC (**left**), A2C (**middle**), and AM (**right**) methods.  
Figure 13 shows the HCV data set with four clusters. The CPC method (left) leads to a clear separation of the different clusters. But the read and blue clusters are attracted to each other. With the A2C method (middle), again, a better, clearer separation is visible. The same applies to the AM method (right).  
The use of the three newly developed CCV techniques has indicated that the results based on the \(k\)-means clustering algorithm deliver more information about the dependencies between the individual clusters when focusing on a single cluster. In general, two  
Figure 11: HCV data set with two clusters and visualized results with the CPC (**left**), A2C (**middle**), and AM (**right**) methods.  
Figure 12: HCV data set with three clusters and visualized results with the CPC (**left**), A2C (**middle**), and AM (**right**) methods.  
Figure 13: HCV data set with four clusters and visualized results with the CPC (**left**), A2C (**middle**), and AM (**right**) methods.  
clusters could be too few for the HCV dataset because there are four categories. With three clusters, the clusters are close together but more or less clearly separated. Four clusters lead to a more or less clear separation with no mixing data points. With the red cluster as the center, all three CCV techniques achieved a good separation of the three other clusters.