## 2 Materials and Problem Statement
### Problem Statement  
Four cases from the available database were considered. These cases were employed to investigate the difference between healthy, epileptic seizure-free, and epileptic seizure states in varying perspectives. These cases can be described as follows:  
* **Case I (Datasets A and, B versus dataset E):** the recognition problem between healthy and epileptic seizure states. In this dataset, EEG segments from datasets A, B, and dataset E were employed, and they were divided into two categories: EEG segments belonging to datasets A and, B, and EEG segments belonging to dataset E.
* **Case II (Datasets C and, D versus dataset E):** the recognition problem between epileptic seizure-free and epileptic seizure states. In this dataset, EEG segments from datasets C, D, and dataset E were employed, and they were divided into two categories: EEG segments belonging to datasets C and, D, and EEG segments belonging to dataset E.
* **Case III (Datasets A and B versus datasets C and D versus dataset E:** used to determine the difference between the healthy, epileptic seizure-free, and epileptic seizure brain states. In this dataset, EEG segments from datasets A and B, EEG segments from datasets C and D, and EEG segments from dataset E were employed. These were divided into three categories: EEG segments belonging to datasets A and B, EEG segments belonging to datasets C and D, and EEG segments belonging to dataset E.
* **Case IV (Dataset A versus dataset B versus dataset C versus dataset D versus dataset E):** focused on an attempt to determine any slight changes in the EEG signals. In this dataset, EEG segments from datasets A, B, C, D, and E were employed, and were divided into five categories: EEG segments belonging to dataset A, EEG segments belonging to dataset B, EEG segments belonging to dataset C, EEG segments belonging to dataset D, and EEG segments belonging to dataset E.  
Almost all studies automatically classify EEG signals into either two classes: healthy (datasets A and B) and epileptic seizure-free (datasets C and D), or two classes: healthy (datasets A and B) and epileptic seizure (dataset E), or three classes: healthy (datasets A and B), epileptic seizure-free (datasets C and D), and epileptic seizure (dataset E). Few studies have used five classes: healthy (two classes, datasets A and B), epileptic seizure-free (two classes, datasets C and D) and epileptic seizure (one class, dataset E). Simultaneously considering all of the above five situations is almost non-existent.  
Figure 1: Typical electroencephalographic (EEG) segments from each of the five datasets (**A–E**).  
Epilepsy, which involves sudden and often unforeseen occurrences, is a neurological condition in which sufferers experience spontaneous seizures that are caused by disturbances in the electrical activity of the brain [1; 2; 3; 44; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44]. In order to deal with these problems, a new theoretical perspective based on a hypothesis is proposed in this paper. The main contributions can be described as follows:  
* The physical meanings of extracted features are very clear. To the best of our knowledge, this method is designed to explain the principle of EEG generation.
* The nonlinear and non-stationary problems are no longer an issue. The original intention of the hypothesis was to solve the nonlinear problem, which was proven by the later experiment results. Additionally, the important part, the LMD, was proven to be a good approach to deal with the non-stationary problem.
* Taking into account all of the recognition tasks. The above five situations were simultaneously considered to verify the correctness and effectiveness of this method, also reflect the generalization ability of EEG signal analysis.