# Affinity Propagation Clustering Using Path Based Similarity
## 3 Results
### Results on UCI Datasets
#### 3.2.1 Clustering results on UCI datasets
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Balance Scale** & **Synthetic Control** & **Glass Identification** & **Mushrooms** \\ \hline EM & 0.5718 \(\pm\) 0.0020 & 0.5950 \(\pm\) 0.0531 & 0.5096 \(\pm\) 0.0291 & 0.6798 \(\pm\) 0.1030 \\ \(k\)-means & 0.5652 \(\pm\) 0.0328 & **0.6662 \(\pm\) 0.0240** & 0.5364 \(\pm\) 0.0234 & 0.7740 \(\pm\) 0.1368 \\ SSC & 0.5728 \(\pm\) 0.0000 & 0.5926 \(\pm\) 0.0000 & 0.4840 \(\pm\) 0.0012 & **0.7934 \(\pm\) 0.0000** \\ pAPC & 0.5638 \(\pm\) 0.0987 & 0.6477 \(\pm\) 0.0000 & 0.4971 \(\pm\) 0.0000 & — \\ APCGD & 0.5829 \(\pm\) 0.1021 & 0.4192 \(\pm\) 0.0000 & 0.4248 \(\pm\) 0.0297 & 0.5781 \(\pm\) 0.0000 \\ APC & 0.5518 \(\pm\) 0.0563 & 0.6350 \(\pm\) 0.0000 & 0.5598 \(\pm\) 0.0000 & 0.7616 \(\pm\) 0.0000 \\ APC-PS & **0.5925 \(\pm\) 0.0018** & **0.6650 \(\pm\) 0.0000** & **0.5620 \(\pm\) 0.0000** & 0.7634 \(\pm\) 0.0000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results (average \(\pm\) standard deviation) on UCI datasets under evaluation metric _Fmeasure_. The numbers in **boldface** denote the best performance. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Balance Scale** & **Synthetic Control** & **Glass Identification** & **Mushrooms** \\ \hline EM & 0.4708 \(\pm\) 0.0130 & 0.5581 \(\pm\) 0.0545 & 0.4516 \(\pm\) 0.0397 & 0.6086 \(\pm\) 0.0828 \\ \(k\)-means & 0.4567 \(\pm\) 0.0241 & 0.6277 \(\pm\) 0.0251 & 0.4775 \(\pm\) 0.0464 & **0.7232 \(\pm\) 0.1106** \\ SSC & 0.4675 \(\pm\) 0.0000 & 0.5664 \(\pm\) 0.0000 & 0.3778 \(\pm\) 0.0005 & 0.6732 \(\pm\) 0.0000 \\ pAPC & 0.5076 \(\pm\) 0.1039 & 0.5664 \(\pm\) 0.0000 & 0.3895 \(\pm\) 0.0000 & — \\ APCGD & 0.5173 \(\pm\) 0.0872 & 0.4750 \(\pm\) 0.0000 & 0.4912 \(\pm\) 0.0239 & 0.5198 \(\pm\) 0.0000 \\ APC & 0.4294 \(\pm\) 0.0449 & 0.6015 \(\pm\) 0.0000 & **0.5606 \(\pm\) 0.0000** & 0.7105 \(\pm\) 0.0000 \\ APC-PS & **0.6539 \(\pm\) 0.0046** & **0.6390 \(\pm\) 0.0000** & 0.5477 \(\pm\) 0.0000 & **0.7277 \(\pm\) 0.0000** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results (average \(\pm\) standard deviation) on four datasets under evaluation metric _F_owlkes-Mallows Index (_FMI_). The numbers in **boldface** denote the best performance. APC based on this similarity. In contrast, APC-PS firstly finds out the exemplar for each cluster using the negative Euclidean distance between samples. Next, it calculates the path-based similarity between the found exemplars and other samples. This observation suggests APC-PS can more correctly find out exemplars than pAPC. APCGD defines a neighborhood graph at first, and then it takes the shortest path between two samples in the graph as the geodesic distance between them. Next, APCGD takes the negative geodesic distance as the similarity between them and performs APC based on this similarity. Obviously, if two samples are directly connected in the graph, the shortest path between two samples is the direct edge. However, it is rather difficult to construct a suitable neighborhood graph for APCGD, and an inappropriate neighborhood graph can bring direct connection between two samples, which belong to two different clusters. Given that, the performance of APCGD often loses to APC-PS.