# Experimenting with Extreme Learning Machine for Biomedical Image Classification
## 1 Introduction and Background  
Since the introduction of the backpropagation algorithm, feedforward neural networks have been extensively utilized and embraced by researchers in both academic and industrial settings. These networks are specifically designed to detect errors by propagating information from the output nodes back to the input nodes [1]. The conventional backpropagation algorithm, being a first-order gradient method for parameter optimization, encounters challenges such as slow convergence and the risk of getting stuck in local minima. To address these issues, researchers have introduced various approaches to enhance the efficiency and optimality of training feedforward neural networks. One notable example is the utilization of second-order optimization methods [2], subset selection methods [3], or global optimization methods [4]. While these methods often result in faster training speeds or an improved generalization performance compared to the backpropagation algorithm, the majority of them are still unable to ensure the attainment of a globally optimal solution. In recent times, there has been a proposal for an approach called extreme learning machine (ELM) to train single hidden layer feedforward neural networks (SLFNs) [5]. ELM introduces a unique approach where the hidden nodes are randomly initialized and remain fixed without any iterative tuning. Interestingly, these hidden nodes in ELM do not necessarily have to resemble neurons. The only parameters that require learning are the connections, specifically the weights between the hidden layer and the output layer. As a result, ELM is formulated as a linear-in-the-parameter model, simplifying the process to solve a linear system. Compared with traditional learning methods for feedforward neural networks, ELM exhibits remarkable efficiency and has a tendency to converge towards a global optimum. Theoretical studies have demonstrated that evenwith randomly generated hidden nodes, ELM preserves the universal approximation capability of single-hidden-layer feedforward networks (SLFNs) [6; 7]. Utilizing commonly employed activation functions, ELM has the capability to achieve an approximate optimal generalization bound similarly to that of traditional feedforward neural networks where all parameters are learned [8; 9]. The superiority of ELM over the traditional feedforward neural network (FNN) algorithms in terms of efficiency and generalization performance has been demonstrated across various problem domains in different fields [7; 10]. It is worth noting that ELM is generally much more efficient than support vector machines (SVMs) [11], least square support vector machines [12], and other state-of-the-art algorithms. Empirical investigations have revealed that the generalization capability of ELM is comparable to, and in some cases even superior to, support vector machines (SVMs) and their variants [7; 13; 14]. Detailed comparisons of ELM and SVM can be found in [PERSON] [15] and [PERSON], [PERSON], et al. [16]. Over the past decade, the theories and applications of ELM have been subject to extensive research. In terms of learning efficiency, the original objectives of ELM encompass three aspects: minimizing human intervention, achieving high learning accuracy, and facilitating a fast learning speed. In recent times, notable advancements have been made in utilizing feedforward neural networks for the classification of medical images [17]. Feedforward neural networks, particularly deep learning, which is a branch of machine learning focused on studying multiple layers of perception, have gained substantial attention in the realm of image classification. Deep learning aims to develop hierarchical representations of features, distinguishing lower-level characteristics from higher-level ones, thereby enabling the identification of various higher-level features. Image classification--categorizing images into predefined groups--is a significant challenge in computer vision.