# Discrimination of Severity of Alzheimer's Disease with Multiscale Entropy Analysis of EEG Dynamics
## 1 Introduction  
Alzheimer's disease (AD) is a neurodegenerative disorder as well as the most prevalent form of age-related dementia in the modern society [1]. As of 2018, there were an estimated 50 million people with AD worldwide. This number will increase to around 82 million in 2030, and 152 million in 2050 [2]. Increasing focus on detecting or differentiating AD using sophisticated analysis of electroencephalography (EEG) signals has emerged in recent years. Optimization of EEG analysis is critical for developing wearable devices to screen the AD patients in low cost and non-invasive manners. Selection of crucial EEG channels can further help in designing new wearable devices and saving computational resource.  
Multiscale entropy (MSE) and MSE-based analyses of EEG signals from AD patients have been explored in many studies [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. MSE measures the complexity of a physiologic time series under different time scales, and reflects the degree of healthiness of a biological system through its outputphysiologic signals [14; 15]. Many studies observed that the MSE values of EEG signals from healthy subjects are higher than those from the AD patients at small scales, while lower than those from the AD patients at large scales [3; 4; 5; 6]. Besides, the slope of MSE vs. scale plot at large scales was found higher for the AD patients than the healthy subjects [6].  
Recently, machine learning technique has been further applied to the EEG analysis to improve the classification performance of the AD patients with different severities, including healthy subjects [7; 8]. Each time scale of MSE may serve as a feature in the machine learning model. [PERSON] et al. adopted 38 features for machine learning for each EEG channel, which included MSE features as well as other spectral and temporal features extracted from the EEG signals. In total, 24 EEG records were collected from healthy, mild AD, and moderate AD groups. Five binary and one ternary classification problems were addressed [8]. [PERSON] et al. adopted 380 MSE features extracted from 19 EEG channels. The EEG signals from each channel contributed a sequence of 20 different MSE values computed at scales 1-20, separately. In total, 123 EEG records were collected from healthy, very mild AD, mild AD, and moderate to severe AD groups. Six binary classification problems were addressed [8].  
Instead of binary or ternary classification, we propose a new AD severity index to measure the degree of AD severity as additional information for clinical doctor by using linear discriminant analysis (LDA). The corresponding machine learning model is so simple that only 2-5 MSE features are required to be extracted from a particular EEG channel. This benefits the extraction of critical time scales as the MSE features in the model.  
In this study, we collected the EEG data recorded from 15 healthy subjects, 69 patients with mild AD, and 15 patients with moderate to severe AD. Our study consisted of three parts. In the first part, we used leave-one-out cross validation (LOOCV) method to test the performance of the LDA in differentiating patients with moderate to severe AD from the healthy subjects. In the second part, we obtained the AD severity index by training with the healthy and moderate to severe AD groups. In the third part, we obtained the AD severity index by training with the healthy and mild AD groups.