# Fingerprint Classification Based on Multilayer Extreme Learning Machines
## 1 Introduction
The standard Extreme Learning Machine (ELM) is characterized by its rapid processing and low computational cost while achieving accuracy levels comparable to those of CNNs [10; 11; 12]. An ELM with a single hidden layer was demonstrated in [13], where a standard ELM was compared to two types of CNNs (a CaffeNet variant and the CNN proposed in [10]) for fingerprint classification. The study found that when using Hong08 [14] as a descriptor and the ELM as a classifier, an accuracy of 94% and a penetration rate of 0.0332 were achieved, compared to the 99% accuracy obtained by the CNNs. ELM networks were proposed by [PERSON] for the training of single-hidden-layer feed-forward neural networks (SLFNs). In ELM, the hidden nodes are initialized randomly, then trained without iterative methods. The weights and hidden neuron biases are randomly assigned, while the output weights are determined using the Moore-Penrose pseudoinverse under the least squares criterion [15]. In ELM, the hidden nodes (or neurons) may or may not be of the same size. The only parameters that need to be learned are the connections (or weights) between the hidden layer and the output layer. Consequently, ELM is formulated as a linear model. In comparison with traditional learning methods such as SVM, CNNs, etc., ELM is notably efficient and tends to achieve a globally optimal solution. Field studies have proven that even with randomly generated hidden nodes, ELM retains the universal approximation capability of SLFNs [16; 17]. M-ELMs are networks formed by extreme learning machine autoencoders (ELM-AEs), proposed as a new multilayer perceptron (MLP) training scheme aimed at addressing the deficiencies of ELMs. Notably, a standard ELM does not perform well when processing natural signals such as sounds and images. In [18], imaging tests were conducted, including car detection, gesture recognition, and incremental online tracking. For car recognition, the UrbanaChampaign dataset from the University of Illinois [19; 20] was used in both the training and testing phases. Images with dimensions of \(100\times 40\) pixels achieved an accuracy of 95.5% with a training time of 46.7 s. In the second experiment, the Cambridge gestures dataset was used [21], comprising 900 image sequences of novel hand gesture types, which are divided into three hand shapes and three movements. Each type contains 100 image sequences with dimensions of \(60\times 80\times 10\) pixels. In the first phase, static gestures were analyzed, while the second phase included movements. This experiment achieved an average test accuracy of 99.4%, with a training time of 57.7 s.  
The M-ELM training architecture is structurally divided into two phases: a hierarchical representation of unsupervised features and a supervised feature classification phase. ELM-AEs are stacked to enable learning across multiple hidden layers (unsupervised), except for the final layer, which consists of a standard ELM (supervised) that performs classification [22]. The M-ELM model was proposed to improve generalization capacity, which directly depends on the characteristics of the training dataset. By addressing the two primary issues of the original ELM--network stability and computational complexity--the M-ELM enhances generalization capacity and simplifies computations. Specifically, the output weights are calculated using the generalized inverse of the hidden-layer output and the system's actual outputs [15]. As mentioned earlier, this study introduces, for the first time, the use of an M-ELM as a fingerprint classifier. To achieve this, we optimize the hyperparameters using brute force and determine the optimal number of neurons for each hidden layer. The results are validated using five-fold cross-validation, employing metrics such as training time, accuracy, and penetration rate [5; 23]. These metrics enable a fair comparison with the most recent studies, highlighting their relevance in the literature [10; 13].