## 1 Introduction  
In pattern recognition systems, efficient methods of feature selection and extraction can reduce the dimensionality problem, thus reducing both the computation time and the memory requirements of the training algorithms [1]. An autoencoder is a feed-forward neural network that builds a compact representation of the input data, and is mainly used for unsupervised learning [2]. It is composed of an encoder and a decoder: the encoder reads the input data and maps them to a lower-dimensionality space, while the decoder reads the compact representation and reconstructs the neural network input. In the same way as for all supervised learning neural networks [34], the core aspect of the training of an autoencoder is the backpropagation algorithm. This algorithm iteratively tunes the weights and biases of the neural network by applying the gradient descent method. Autoencoder networks are in great demand in multiple applications in modern society, for example, for dimensionality reduction, image retrieval, denoising, and data augmentation [2]. Several works in the literature have developed feature extraction methods using autoencoders and backpropagation. A comparative study between the performance of a traditional autoencoder and a denoising sparse autoencoder is presented in [5]. Another widely used architecture is the stacked autoencoder, which includes the stacked denoising sparse autoencoder [6] and the symmetric stacked autoencoder with shared weights [7]. Semi-supervised learning algorithms have also been used as autoencoder training algorithms [8; 9]. However, the backpropagation training technique limits the generalization ability of the autoencoder, which results in low computational efficiency and the presence of local optima. An extreme learning machine (ELM) is an emerging training paradigm for neural networks which includes supervised [10], semi-supervised [11], and unsupervised training [12]. The fundamental principle of this architecture is the random assignment of weights and biases in the hidden layer and the analytical determination of the weights of the output layer, in which the least squares method is applied to a system of linear equations [13; 14]. The simplicity of the model, the lower numbers of training parameters, the low convergence speed, and its high generalization capacity mean that ELM neural networks have advantages for classification, regression, and clustering problems. Variants such as the kernel-ELM (K-ELM) [15], due to the significant reduction in the number of parameters and the increase in the training speed, and the online sequential ELM [16], due to its capacity to process batches of data, can even deal efficiently with problems involving large volumes of data. In the field of rolling element fault diagnosis, ELM can also solve the problem of weak signals caused by long transmission paths [17]; for example, the novel method presented in [18] can help in frame feature selection for ELM. In computer vision, the researchers of [19] proposed a visual object tracking scheme with promising results. On the other hand, to handle the problems that local minima can cause, some studies have used heuristic optimization techniques to estimate the network parameters, such as differential evolution, particle swarming (PSO), and genetic algorithms [20]. These heuristic algorithms always search for the global minimum of the objective function and are efficient in several research fields, as is the case for the PSO algorithm that adjusts the parameters of an underactuated surface search model [21]. An improved scheme of this method integrates the PSO with global optimization capability, a 3-Opt algorithm with local search capability, and a fuzzy system with fuzzy reasoning ability [22]. The probabilistic and colony algorithm is another optimization technique integrated into the architecture of an ELM network [23].