# Fingerprint Classification Based on Multilayer Extreme Learning Machines
## 5 Results and Discussion
### Complexity Analysis  
Another important parameter to consider when comparing different learning techniques is the computational cost, particularly the training time. The computational complexity of the proposed models was evaluated on a computer equipped with an Intel(r) Core(tm) i7-6700 processor, 8 GB of RAM, and a 64-bit Windows 10 operating system (Santa Clara, CA, USA). Table 4 reports the training times (in seconds), along with the sample mean and standard deviation, for different fingerprint qualities. A total of 1000 simulations were conducted to ensure representative results for each case to validate the observations. It is important to mention that the results presented for [10] were directly replicated using high-performance hardware--specifically an Nvidia GeForce GTX TITAN GPU (2688 cores, 6144 MB GDDR5 RAM) and a 2.6 GHz Intel Core i5 processor with 4 GB of RAM (Santa Clara, CA, USA). Regarding the software environment, [PERSON] et al. [10] employed the C++ Caffe library, a low-level language offering faster execution than the programming language utilized in this study (MATLAB 2024a). Given the focus of this work on ELMs and acknowledging the hardware and software limitations compared to the CNN-based model, a complexity analysis was performed. Our method is notoriously disadvantaged in terms of hardware/software. As demonstrated in Table 4, the ELM architecture with three hidden layers emerges as the optimal alternative in this study, a conclusion supported by the performance metrics discussed in the preceding subsection. Although the three-layer ELM (ELM-M3) is more computationally expensive than the original ELM, it is significantly more efficient in terms of computational cost compared to ELM-M2, the unbalanced ELM, and the CNN-based approach (Figure 14). Notably, the computational cost of ELM-M3 is influenced by fingerprint quality, as its performance-optimizing hyperparameters are dependent on the SFINGE database, which accounts for variations in quality. These observations are supported by the number of neurons used in each artificial intelligence approach, as detailed in Table 5. As anticipated, learning time is directly proportional to the model's parameters. Considering the dual objectives of simplicity and performance, the proposed ELM-M3 emerges as the most viable alternative for fingerprint classification. While deeper architectures like ELM-M3 may offer improvements in classification accuracy, it is important to consider the trade-offs associated with their increased complexity. For example, longer training times and a higher number of hidden neurons may result in higher inference times, especially in real-time systems. The ELM-M3 model employs 1250 hidden neurons distributed across three layers, which contributes to its improved performance. However, the increased complexity also comes with higher computational costs. This trade-off is particularly relevant when considering real-world applications, where inference time and system efficiency are critical. On the other hand, when comparing the results obtained by the ELM with three hidden layers with the work of [PERSON] et al. [13], an improvement of 0.034 in accuracy is observed. However, the penetration rate of the pro