Alzheimer's disease (AD) is a neurodegenerative disorder that accounts for nearly 70% of the estimated over 50 million dementia cases worldwide, with a projection for this number to triple by 2050 [1]. Approximately, 10 million new cases are registered worldwide each year, as reported by the World Health Organization [2]. While there is no cure for AD, early diagnosis and precise characterization of disease progression can improve the quality of life for AD patients and their caregivers.

Taking the United States of America as a reference to obtain an objective statistical sample, it can be observed that out of 6.5 million Americans suffering from Alzheimer's disease (AD) in 2022, 27% of that number are between 64 and 74 years old, while 35.7% are over 85 years old [3]. It is clear that age is a determining factor in the development of the disease, with a proportional increase observed. Taking the specific case of Spain, it can be observed that an estimated 40,000 new cases of dementia are diagnosed each year, and of these, around 800,000 people suffer from AD, according to estimates from the Spanish Neurology Society (SEN) [4]. Recent population studies indicate prevalences of dementia ranging from 9.4% to 8.5% [5], [6] in those over 70 years old, and between 5.5% and 5.8% [7], [8] in those over 65 years old. The latest statistics from the spanish national institute of statistics (INE) on causes of death for 2020 report a total of 15,571 deaths due to Alzheimer's disease in Spain, following a sustained increase in recent decades parallel to the aging of the population. In addition, it is important to mention that the disease has a higher incidence in women, representing the 3.15% of all deaths in Spain caused by AD. Consequently, it can be concluded that gender is also a determining factor.

The term dementia is used to characterize various neurodegenerative disorders caused by damage and death of neurons, resulting in an impairment of cognitive and behavioral functions. Among the different forms of dementia, Alzheimer's disease is the most common [3]. The main symptoms of AD are difficulty in remembering conversations, names, or recent events, which is often an early symptom; apathy and depression are also often early symptoms. Later symptoms include communication problems, disorientation, confusion, misjudgment, behavioral changes, and ultimately difficulty in speaking, swallowing, and walking. Furthermore, recent autopsy studies show that over half of people with AD have dementia as well as brain changes [1].

According to the symptomatology, Alzheimer's disease has been divided into three stages: preclinical, mild cognitive impairment, and Alzheimer's dementia [9].

Preclinical AD: Changes in the brain, blood, and cerebrospinal fluid related to AD begin to occur, but the patient does not show any symptoms. This phase can start up to years or decades before the first clinical symptoms of dementia [10]. Detecting AD in this preclinical stage would offer a crucial opportunity for therapeutic interventions [11]. Mild Cognitive Impairment (MCI): In this early stage, the person still behaves independently, but may feel some memory lapses and have difficulty finding the right word or remembering the location of familiar places. Friends and family may notice these small difficulties. This stage is often referred to as mild or early-stage Alzheimer's disease. The term MCI has often been used in research trials with the goal of including as many people as possible with symptoms that were not severe enough to meet current diagnostic criteria for Alzheimer's disease, but who may do so at some point. However, it has been observed that 30% of subjects diagnosed with MCI will not progress to Alzheimer's dementia in the near future [12]. Alzheimer's Dementia: The patient's ability to function in daily life is affected by deficiencies in memory, thinking, and behavior [12]. This stage is further subdivided into two different stages: 1) Moderate or mid-stage Alzheimer's disease (ADM). In this phase, which is usually the longest, the person may experience greater difficulties in performing daily tasks such as paying bills, remembering their own address, dressing themselves, or controlling their bladder and bowels. The patient notices these symptoms, leading to frustration and anger. Additionally, in this stage, some psychological symptoms begin to appear, such as suspicion, delusions, or compulsive behavior [12]. 2) Advanced or Late-stage Alzheimer's disease (ADA). In this final stage, people begin to lose their ability to interact with their environment and their memory and cognitive abilities are severely affected. At this stage, the patient requires 24-hour personal care [13].

Our study focuses on the prediction of patients with moderate or advanced stages of AD, since in these cases the dependence of patients is more severe. Currently, the diagnosis of Alzheimer's disease is carried out using standardized mental state exams, which are commonly assisted by costly neuroimaging scans and invasive laboratory tests, making the diagnosis slow and expensive. However, in the last decade, electroencephalography (EEG) has emerged as a non-invasive alternative technique for studying Alzheimer's disease, competing with more expensive neuroimaging tools such as magnetic resonance imaging (MRI) and positron emission tomography (PET) [14]. In addition, EEG is ideal for the analysis of Alzheimer's disease in early stages [15].

Likewise, there are different types of machine learning models that can applied to EEG data, or other type of information. The main categories are divided depending on the type of action performed [16]. Classification: a classification model can analyze the data of the brain's electrical activity and classify them into different categories. For example, a classification model can distinguish between different mental states, such as sleep and wakefulness, or between different types of brain activity, such as alpha waves and beta waves. Some of the most commonly used classification algorithms are Support Vector Machine (SVM), Bayesian Linear Discriminant Analysis (BLDA), Decision Trees (DT), Gaussian Naive Bayes (GNB) [16]. Regression: a regression model can be used to analyze data from brain electrical activity and predict future values. For example, a regression model can be used to predict a person's stress level based on their brain activity at a given moment. Some of the most commonly used regression algorithms are k-Nearest Neighbors (KNN), Random Forest (RF), and eXtreme Gradient Boosting (XGB) [16]. Clustering: a clustering model can analyze data from brain electrical activity and group them into different clusters. For example, a clustering model can be used to group people based on their patterns of brain activity and discover similarities or differences among them. Some of the most commonly used clustering algorithms are Hierarchical Clustering, K-Means, k-Medoids, Self-Organizing Map, Fuzzy c-Means, and Gaussian Mixture [16].

Machine learning models can be trained and optimized using techniques such as supervised learning and unsupervised learning. Once trained, the models can be used to analyze data in real-time and provide accurate and detailed results about brain activity [17].

In this study, deep learning algorithms, which are a subset of machine learning composed of deep Artificial Neural Networks (ANN), were employed. These networks present multiple layers with interconnected nodes, called “neurons”, that process and transmit information. In an ANN, the innermost layers (called hidden layers) learn complex and abstract representations of the data as information is transmitted through the network. Overall, ANNs are capable of learning complex patterns in data and provide very high accuracy performance in machine learning problems due to their ability to learn abstract representations of data. Some commonly used deep learning topologies are Convolutional Neural Networks (CNN) and recurrent neural networks (RNN) [18], [19].

As it will be shown, the neuronal network proposed allows for the improvement and refinement of AD detection in patients in middle and advanced stages of the disease, achieving an accuracy of over 95% in detection by using Radial Basis Function (RBF) neural network algorithms initialized with fuzzy logic. These functions are centered on specific points called centroids and their output depends on the Euclidean distance between the input point and the centroid. The proposed algorithm allows the network to learn complex patterns and better generalize responses for unknown data, by using fuzzy logic. This new initialization procedure improves the performance of classical algorithms, since it assigns membership probabilities that provides greater precision during the optimization. In addition, data from different medical centers and a population sample of more than 650 patients from five different hospitals have been analyzed to validate the proposed method. The interhospital nature of the study and the large number of patients analyzed confer great relevance and robustness to the study presented.

The article is organized as follows: Section 2 presents the materials used in this study. Section 3 presents the proposed classification approach, the description of the proposed network, and the validation method employed. Results and their discussion are shown in Sections 4 and 5, respectively. Finally, the conclusions of this work are summarized in Section 6.