# Fingerprint Classification Based on Multilayer Extreme Learning Machines
## 5 Results and Discussion
### Evaluation and Performance Comparison with the State of the Art  
Recent studies have employed ELMs for biometric classification tasks, such as fingerprint and [10; 13; 33; 34] palm vein recognition [2], with an emphasis on age and gender detection using single-layer ELMs that include a regularization parameter. In order to compare our proposal with the most recent and important studies reported in the literature, performance metrics such as accuracy (overall performance of all classes) and penetration rate (performance of each class) are considered, making this comparison more conclusive. Table 3 compares the results obtained in this work using the Hong08 descriptor with the performances reported by [PERSON] et al. [10] and [PERSON] et al. [13]. The results of [33; 34] are omitted. The work by [PERSON] et al. [10] achieved an accuracy of 98.7% but only considered a DB of scare fingerprint samples (FVC-2004 with 880 samples). Moreover, details about the ELM algorithm (hyperparameters) were not exposed, since the study focused on the fingerprint feature descriptor. The second study, apart from obtaining lower accuracy results (83.45%), performed heuristic optimization considering a lower number of hidden nodes than the number of training samples for the SFINGE database, meaning that optimization presented local and not global maxima. On the one hand, it is appreciated that the work based on a CNN [10] achieved the best performance for both accuracy (99.6%) and the absolute value of the penetration rate (0.31). This is practically perfect if the fingerprint is acquired in an ideal manner (HQNoPert). The superiority of the approach proposed in [10] is distinguishable for all fingerprint qualities, being only 0.02 better in terms of accuracy and 0.03 in terms of PT than the three-hidden-layer ELM proposed in this paper. The CNN developed by [PERSON] et al. [10], which incorporates a modified version of AlexNet with softmax functions, demonstrates superior performance compared to the architecture proposed in this study. The AlexNet architecture is characterized by five convolutional hidden layers and three fully connected hidden layers, designed based on the ELM algorithm. In [10], modifications were made to the number of units within the network to simplify the search space during training and enhance both the speed and convergence of the process. The network was trained using the stochastic gradient descent (SGD) algorithm, which reduced computational costs by utilizing only a subset of training instances in each iteration. This approach introduces a bias in error calculation relative to the optimum but significantly accelerates the process. In addition, this network is used together with images to classify fingerprints without requiring an explicit feature extraction process. This approach addresses challenges associated with noise or distorted fingerprint images more effectively than our proposed method, which relies on descriptor layers based on an ELM. While our approach demonstrates a 0.04 improvement in accuracy compared to the unbalanced ELM method characterized by the golden ratio, as proposed by [PERSON] [13], it exhibits a marginal disadvantage of 0.0003 in terms of PR. This slight drawback can be attributed to variance in the sample mean of the measurements. When evaluating performance relative to fingerprint quality (independent of the classification model), it is evident that fingerprints of the highest quality (HQNoPert) achieve approximately 0.02 higher accuracy and 0.05 higher Pr rates compared to those of average quality (default). Similarly, HQNoPert