# Improved Selective Deep-Learning-Based Clustering Ensemble
## 4 Experiments
### Experimental Settings and Clustering Performance Comparison  
In this section, we compare the proposed ISDCE algorithm with 11 comparison algorithms, i.e., WSCE [21], PTAAL, PTACL, PTASL [19], PTGP [19], SECWK [22], LWEA [23], LWGP [23], LRTA [24], ECCMS [25], and SPACE [26]. For the 11 comparison algorithms, the parameters will be set as suggested by their corresponding papers. The total number of base clusterings is 50. The number of base clusterings involved in the ensemble is 20. For each algorithm, the final number of clusters was set to the true number of categories on the dataset. The running time of the algorithm is 20. The NMI, ARI, mean, and variance of the 20 running results were used as the evaluation results. For our proposed ISDCE algorithm, the initial ensemble size S = 50 and the top M is in the range of [10, \(\frac{S}{2}\)]. The number of clusters \(k\) was set to the true number of categories on the dataset. The parameter \(\theta\), which adjusts for the effects of cluster uncertainty, was set uniformly to 0.4 (a range of [0.2, 1] is recommended). Here, we experimented with three selective strategies (quality strategy, diversity strategy, and balance strategy) in the ISDCE, where the adjustment factor \(\beta=0.5\) in the balance strategy. Regarding the parameter settings for deep base clustering, we used randomly initialized network parameters. The optimizer is uniformly Adam and the activation function is RELU, The corresponding autoencoder network structure for the experimental data is: Cars--[8,8,6], Iris--[4,4,4], Wine--[13,12,10], Mnist5--[784,500,500,2000,10], MNIST--[784,500,500,2000,10], Strain--[200,100,30], Species--[232,100,30]. The clustering performance comparison result is shown in Tables 2-5. For each dataset, we ran it 20 times and computed average and standard deviation result for evaluation measures. All the bolded results in Tables 2-5 are statistically (according to pair-wise \(t\)-test at 95% significance level) superior to the other methods. ISDCEQS denotes that ISDCE uses quality strategy for ensemble, and ISDCEDS indicates that ISDCE adopts diversity strategy for ensemble. ISDCEBS represents that ISDCE employs balance strategy for ensemble. Tables 2 and 3 show the clustering performance of three UCI datasets. For each dataset, the highest three scores are highlighted in bold. As can be seen from the NMI results, three strategies of ISDCE achieved the highest score, except for the Cars dataset. SPACE achieved the best NMI on the Cars dataset, but its ARI value is obviously lower than ISDCE in Table 3. This shows that the ISDCE method, especially ISDCEDS, has a better clustering performance and better robustness. In addition to the Cars dataset, three strategies of ISDCE achieved the best ARI scores on the other two datasets. ISDCEDS achieved the best ARI on the Cars dataset, but ISDCQS and ISDCEBS seem to not be good enough. The reason for why ISDCEDS has a much larger value than other methods may be that, for Cars data, rich ensemble diversity may have its main role in the integration process. ISDCEDS utilizes the rich diversity of base partitions to integrally generate better consensus clustering results. LWEA, LWGP, and ECCMS perform better than ISDCEQS and ISDCEBS, while they perform far worse than ISDCEDS. In comparison experiments on these three small UCI data, we observe that all methods, except for the LRTA and SPACE method, obtain clustering results in less than 1 s. This indicates that these methods can obtain the final ensemble results quickly at a small data scale. Tables 4 and 5 show the clustering performance of two image datasets and two biological datasets. \"**timeout**\" means that the clustering results were not obtained for a long time. \"**error**\" means that, when the eigs function was calculated, dnaupd did not find any eigenvalues that achieved sufficient accuracy using the WSCE method. As can be seen from the NMI results in Table 4, three strategies of ISDCE achieved the best NMI scores on all image and biological datasets.