# Agglomerative Clustering with Threshold Optimization via Extreme Value Theory
## 5 Experimental Results
### Deep Clustering  
Recent work [10; 11] proposes an unsupervised feature learning approach, combining self-supervision and clustering to capture complementary statistics from large-scale data. During network training, the traditional clustering algorithms with hand-tuned parameters K-Means [22] and PIC [30] are used to cluster features at every epoch. We replace these clustering algorithms with the specified approach (AHC, FINCH, PEACH) and train for 100 epochs.  
We report the deep clustering results for training the ILSVRC 2012 validation set in Table 4. When used alongside network training to cluster features at each epoch for an unsupervised deep learning approach, PEACH provides the best results. The improvement over FINCH would be even great if we would not have manually selected the best partition. More sensitive parameter-dependent algorithms are worse with bad guesses when used  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**Param. Dep.**} & \multirow{2}{*}{\begin{tabular}{c} **Approach** \\ _GT_\# _Classes_ \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Out-of-Distribution** \\ _ImageNet:166_ \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **In-Distribution** \\ _ImageNet:1000_ \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Mixed-Distribution** \\ _ImageNet:1166_ \\ \end{tabular} } \\ \cline{2-10}  & & **\#C** & **NMI** & \(\mathbf{B^{3}}\) & **\#C** & **NMI** & \(\mathbf{B^{3}}\) & **\#C** & **NMI** & \(\mathbf{B^{3}}\) \\ \hline Ground-truth & K-Means & given & 0.643 & 0.268 & given & 0.825 & 0.576 & given & 0.755 & 0.367 \\ Ground-truth & Spectral & given & 0.798 & 0.609 & given & 0.630 & 0.298 & given & 0.763 & 0.367 \\ Ground-truth & BIRCH & given & 0.798 & 0.573 & given & 0.832 & 0.545 & given & 0.808 & 0.468 \\ Ground-truth & AHC [32] & given & 0.632 & 0.253 & given & 0.805 & 0.444 & given & 0.730 & 0.264 \\ \hline Closest to GT & FINCH [4] & 247 & 0.819 & 0.604 & **1018** & 0.821 & 0.575 & 1441 & 0.768 & 0.343 \\ \hline Automatic & **PEACH(\(\mathbf{\tau}_{r}\))** & **265** & **0.822** & **0.662** & 896 & **0.863** & **0.813** & **1031** & **0.837** & **0.487** \\ \hline \end{tabular}
\end{table}
Table 2: _Clustering for Out/In/Mix Distribution ImageNet data._ This table shows NMI and \(B^{3}\) F-scores on ImageNet 2010 and 2012 validation sets with 166 (Out-of-Distribution data), 1000 (In-Distribution data), and 1166 classes (Mixed-Distribution data). We mark the second-best and **best results**, as well as algorithms that optimize parameters on the test set.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **30 K** & **30 U** & **118 K** & **118 U** \\ \hline Large Spectral Clustering & 0.733 & 0.655 & — & — \\ KL-divergence Contrastive & 0.750 & 0.715 & — & — \\ MetaClassification Likelihood & 0.762 & 0.765 & — & — \\ Deep Transfer Clustering & 0.791 & 0.786 & 0.38 & 0.53 \\ FINCH(_Best_) ResNet-18 & 0.696 & — & 0.63 & — \\ PEACH(\(\mathbf{\tau}_{r}\)) ResNet-18 & — & **0.818** & — & **0.68** \\ \hline \end{tabular}
\end{table}
Table 3: _PEACH Transfer Clustering._ This table shows NMI on transfer clustering for ImageNet with partitions from [67] with either 800 training and 82 validation classes and three random samples with 30 classes for testing, or 882 training and 118 test classes. Results with **K** used the ground-truth number of clusters, while **U** indicates estimated cluster counts, partially by [5]. We mark the **best results.  
inside of deep- and deeper-clusters. This highlights that clustering approaches like PEACH are indispensable since it is impossible to know beforehand how many classes are present in unsupervised learning. We also report the top-1 accuracy of deep clustering on MNIST in Table 5, which shows PEACH outperforms K-Means and FINCH at mature epochs.