# Affinity Propagation Clustering Using Path Based Similarity
## 3 Results
### Results on UCI Datasets
#### 3.2.2 Sensitivity of \(p\) on APC and APC-PS  
In this section, we investigate the sensitivity of APC and APC-PS on the input values of \(p\). For this purpose, we vary \(p\) from \(-100\) to \(-10\) on Balance and vary \(p\) from \(-200\) to \(-110\), since the number of exemplars is equal (or close) to \(k\) in the chosen range.  
From Figure 3, we can easy see APC-PS is always significantly better than APC on the Balance scale dataset across the specified range of \(p\), irrespective of F-measure or FMI. In practice, both APC and APC-PS initially identify the same exemplars, but their results are quite different. The cause is that APC-PS uses the path-based similarity to assign a non-exemplar sample to a cluster, whose exemplar is most similar to the non-exemplar sample. In contrast, APC takes the negative Euclidean distance between two samples as the similarity between them and it assigns a non-exemplar sample to its most similar exemplar based on this similarity. This observation justifies our motivation to incorporate the path-based similarity to improve the performance of APC. In addition, we can find the performance of APC-PS in Figure 3 keeps relatively stable, whereas the performance of APC fluctuates sharply. This fact further demonstrates the path-based similarity not only helps exploring the underlying structure between samples, but also helps achieving stable results.  
As to Figure 4, APC-PS also always produce higher results than APC on Synthetic control chart time series dataset. In fact, both APC and APC-PS are also based on the same exemplars. The performance difference between APC-PS and APC indicates the samples in Balance scale dataset and Synthetic control chart time series dataset are distributed with complex structures. These results again suggest that solely utilizing negative Euclidean distance based similarity between samples to assign non-center samples to a cluster is not so reasonable, and this similarity can assign a sample, far away from its cluster center but close to other samples in the cluster, to another cluster, whose exemplar has large similarity with the sample. On the other hand, APC-PS employs a path-based similarity,  
Figure 3: APC and APC-PS on Balance scale dataset under different values of \(p\). (**a**) F-measure; (**b**) FMI.  
This similarity combines negative Euclidean distance based similarity and path-based similarity between exemplars and non-exemplar samples. For samples far away from a target exemplar, APC-PS considers the connection between non-exemplar samples and the exemplar. And hence, the path-based similarity can explore the structure of samples, and help APC-PS to achieve better results than APC.  
Another interesting observation is that APC-PS in Figure 4 does not show as stable results as that in Figure 4. APC-PS fluctuates similarly as APC in Figure 4. One explanation is that the identified exemplars are changed as \(p\) varying. \(p\) also influences the availability matrix \(\mathbf{A}\) and response matrix \(\mathbf{R}\). However, since APC-PS additionally employs the path-based similarity, it still correctly assigns more samples to their respective clusters, thus it gets better results than APC. In summary, we can say that APC-PS is more robust to input values of \(p\) than APC.