## 3 Evaluation
### Experimental Setup
#### 3.2.1 Semi-Supervised Clustering Setting  
In the semi-supervised clustering setting, we measured the performance of clustering original test (unlabeled) samples (\(D^{Ts}\)) (without transformation) and clustering transformed test (unlabeled) samples (\(\tilde{D^{Ts}}\)) (using our model trained on the few labeled samples). As a clustering algorithm, we used the K-means algorithm [43] with different centroid initialization methods, K-means++ [71], random, and PCA-based (where we calculated the principal component analysis for each sample in the test set and performed the K-means algorithm on the PCA components). We calculated the clustering evaluation metrics, listed below, for each clustering scenario. The experiment is repeated for each test set of the five datasets and results are presented in Table 3. Besides the clustering evaluation metrics, we calculated the clustering time for each scenario (without and with our model). **Clustering Metrics. ** We used various clustering metrics that relate to within-cluster and between-cluster measures that related to the compactness and separability properties of the targets. The metrics used and their mathematical formulations are listed below. * _Inertia_[43]: Within-cluster sum-of-squares criterion. \[\sum_{i=0}^{n}\min_{H_{j}\in\mathbb{C}}\left(\|x_{i}-,\mu_{j}\|^{2}\right)\] (6)
* _Homogeneity, Completeness, and V-Measure_[72]: Homogeneity measures a score that each cluster contains only members of a single class. Completeness measures a score that all data points of the same class are assigned to the same cluster. V-Measure measures how successfully homogeneity and completeness have been satisfied. \[V_{\beta}=\frac{(1+\beta)\times H\times C}{\beta\times H+C}\] (7)
* _Adjusted Rand Index (ARI)_[73]: Measures the similarity of two assignments (ground truth and predicted cluster assignment), ignoring permutations. \[\text{RI}\ =\ \frac{a\ +\ b}{C_{2}^{n_{sample}}}\] (8) \[ARI=\frac{\text{RI}-E[\text{RI}]}{\text{max}(\text{RI})-E[\text{RI}]}\] (9)* _Adjusted Mutual Information (AMI)_[74]: Measures the agreement of two assignments (ground truth and predicted cluster assignment), ignoring permutations. Given two cluster assignments \(U\) and \(V\), their entropies, mutual information, and adjusted mutual information are defined respectively as: \[H(U)=-\sum_{i=1}^{|U|}P(i)\log P(i)\] (10) where \(P(i)=|U_{i}|/N\) is the probability that an object picked from \(U\) at random belongs to class \(U_{i}\). Same for \(P^{\prime}(j)\) and \(V\). \[H(V)=-\sum_{j=1}^{|V|}P^{\prime}(j)\log P^{\prime}(j)\] (11) \[\text{MI}(U,V)=\sum_{i=1}^{|U|}\sum_{j=1}^{|V|}P^{\prime\prime}(i,j)\log \frac{P^{\prime\prime}(i,j)}{P(i)P^{\prime}(j)}\] (12) where \(P^{\prime\prime}(i,j)=\left|U_{i}\cap V_{j}\right|/N\) is the joint probability that an object picked at random belongs to both classes \(U_{i}\) and \(V_{j}\). \[\text{AMI}=\frac{\text{MI}-E[\text{MI}]}{mean(H(U),H(V))-E[\text{MI}]}\] (13) where \(E\) is the expected value of the mutual information. * _Silhouette Coefficient_[75]: The silhouette coefficient for a single data point is defined as follows: \[S=\frac{b-a}{max(a,b)}\] (14) where \(a\) is the mean distance between the data point and all other points within the same cluster and \(b\) is the mean distance between the data point and all other points in the nearest cluster. The mean silhouette coefficient is calculated for all data points, and the higher the score, the better the defined clusters indicating a lower within-cluster distance and a higher between-cluster distance. As can be seen from Table 3, using our model to map the test set consistently yielded the best results in all clustering performance metrics over all used datasets. An improvement in both the inertia of clusters and the silhouette coefficient indicates that our model achieves its goal of promoting compactness (within-class) and separability (between-class) of data points which subsequently improves all other clustering metrics.