# Agglomerative Clustering with Threshold Optimization via Extreme Value Theory
## 8 Conclusions  
In most problems, one cannot know the number of clusters or choose between potential clustering options--real-world problems, especially in computer vision, need fully automatic clustering. This paper introduced our Provable Extreme-value Agglomerative Clustering-threshold Estimation (PEACE), and the fully automated PEACH, which applies \begin{table}
\begin{tabular}{c c c} \hline \hline
**Partition** & **\# Clusters** & **NMI** \\ \hline
1 & 13406 & 0.833 \\
2 & 3223 & 0.892 \\
3 & 880 & 0.894 \\
4 & 208 & 0.803 \\
5 & 43 & 0.642 \\
6 & 10 & 0.439 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: _Sensitivity of FINCH to Partition Selection._ In this table, we show the NMI scores of FINCH scores and the number of clusters of each FINCH partition. In our optimistic evaluation of Table 1, we manually selected partition three since the number of clusters of this partition is 880, which is the closest one to the ground-truth 1845. If we would not have the ground-truth but pick a random partition, the resulting NMI values could drop dramatically. In all experiments in this work, we always chose the FINCH partition closest to the ground-truth. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**NMI** & **IJ32** & **IJ64** & **IJ128** & **IJ256** & **IJ512** & **IJ1024** & **IJ1845** & **OLFW** & **IN166** & **IN1000** & **IN1166** \\ \hline \(\tau_{t}=\) & 0.456 & 0.513 & 0.467 & 0.467 & 0.471 & 0.448 & 0.424 & 0.507 & 0.597 & 0.502 & 0.454 \\ \hline PET-FINCH & 0.851 & 0.874 & 0.865 & 0.876 & 0.888 & 0.892 & 0.892 & 0.894 & 0.852 & **0.821** & 0.798 \\ PEACH(\(\tau_{t}\)) & **0.963** & **0.958** & **0.963** & **0.960** & **0.950** & **0.951** & **0.952** & **0.933** & **0.870** & 0.812 & **0.812** \\ \hline \hline \end{tabular}
\end{table} 
Table 11: _PET-FINCH._ In this table, we show the NMI scores of FINCH partition which were selected by using our \(\tau_{t}\). We estimate the number of clusters of AHC by using \(\tau_{t}\) and then we choose the FINCH partition, which is closest to the estimated number of clusters. We compare the results with PEACH. We mark the **best results**. the fully automatic clustering threshold to classic agglomerative clustering. We proved that nearest neighbors of correct links follow a EVT-distribution, in particular a Weibull distribution, and used that to derive a threshold, and then develop a more robust threshold with heuristics automatically reducing an outlier's impact. We also show empirically _that this approach can select the best partition for FINCH_[4], the current state of the art in a visual clustering algorithm. For evaluation, we focused on clustering deep features relevant for advancing the state of the art in vision. Our experiments show that PEACH significantly advances the state of the art in clustering through outperforming recent results from top venues [2; 4; 5; 10; 11; 68; 69; 70]. Looking across all of the different experimental domains, distribution, and problems, PEACH was consistently better than FINCH and other algorithms. We encourage downloading our Github code (released after acceptance) and try either PET-FINCH or PEACH on your problem. If you like the previous state of the art, FINCH, then free yourself from the selection problem with PET-FINCH with virtually no change to your code. However, also note that PEACH offers superior performance, advancing the state of clustering, as well as providing fully automatic parameter selection. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/a15050170/s1](https://www.mdpi.com/article/10.3390/a15050170/s1)]([https://www.mdpi.com/article/10.3390/a15050170/s1](https://www.mdpi.com/article/10.3390/a15050170/s1)), Figure S1: Weibull fit and resulting \(\tau\). Example plots showing Weibull fit and resulting threshold \(\tau\) estimated from the distribution of ANN distances.