# Fingerprint Classification Based on Multilayer Extreme Learning Machines
## 5 Results and Discussion
### Hyperparameter Optimization
The optimization results for the three-hidden-layer M-ELM model are shown in Figures 11-13, where different descriptors and fingerprint qualities are considered to ensure robustness in the findings. The results exhibit a volumetric irregularity in the optimized hidden-node values, with accuracy approaching 1. To achieve efficient generalization, a simple architecture is selected; each figure includes an arrow to indicate the relevant feature. In addition, for visualization purposes, the desired accuracies are highlighted with larger characters (cloud of squares). Once more, it is observed that as additional hidden layers are incorporated, the number of required neurons decreases. This reduction is attributed to the fact that the initial layers are responsible for extracting the primary features of the fingerprints. Figure 7: The accuracy vs. the number of hidden neurons of the original ELM in the training and validation phases when the descriptor corresponds to Liu10. Figure 8: Accuracy in terms of the number of neurons of the two-layer hidden ELM considering the Capelli02 descriptor and the (**a**) default, (**b**) HQNoPert, and (**c**) VQAndPert databases. Figure 9: Accuracy in terms of the number of neurons of the ELM of two hidden layers considering the Hong08 descriptor and the (**a**) default, (**b**) HQNoPert, and (**c**) VQAndPert databases. Figure 10: Accuracy as a function of the number of neurons of the two-hidden-layer ELM considering the Liu10 descriptor and the (**a**) default, (**b**) HQNoPert, and (**c**) VQAndPert databases. Figure 11: Accuracy as a function of the number of neurons of the three-hidden-layer ELM, taking into account the Capelli02 descriptor and the (**a**) default, (**b**) HQNoPert, and (**c**) VQAndPert databases. Figure 12: Accuracy as a function of the number of neurons of the three-hidden-layer ELM, taking into account the Hong08 descriptor and the (**a**) default, (**b**) HQNoPert, and (**c**) VQAndPert databases. The accuracy of the optimized hyperparameters for the various ELM models is summarized in Table 1. Notably, the Hong08 descriptor, coupled with high-quality fingerprints (HQNoPert), yields the best performance. Moreover, the addition of a second hidden layer generally improves the classification accuracy by approximately 0.02 compared to the original ELM. The introduction of a third hidden layer further increases accuracy by an additional 0.01. The absolute values of the penetration rates for different ELM models are  
Figure 5:0 Accuracy as a function of the number of neurons of the three-hidden-layer ELM, taking into account the Liu10 descriptor and the (**a**) default, (**b**) HQNoPert, and (**c**) VQAndPert databases. provided in Table 2, considering the various descriptors (Capelli02, Hong08, and Liu10) and fingerprint qualities (default, HQNoPert, and VQAndPert). These results demonstrate the robustness of the proposed models in dealing with imbalanced learning problems, where success in the minority class is as important as in the majority class. The Hong08 descriptor demonstrates notable performance across various fingerprint qualities, similar to its behavior with accuracy metrics. Specifically, the improvement in the absolute value of the penetration rate achieved by the two-hidden-layer ELM compared to the original ELM (independent of fingerprint quality) is 0.0045, while the difference between the two- and three-hidden-layer ELMs is 0.0055. Consequently, only the results associated with the Hong08 descriptor are considered in subsequent analyses. In contrast, the worst performance is observed using the Capelli02 descriptor, not only across all fingerprint qualities but also across all evaluated metrics. This limitation arises from the method applied in Capelli02, which combines two approaches based on feature extraction via orientation maps (OMs).