## 3 Proposed Method
### Problem Formulation and the Design  
Consider a segment (trial/epoch) of an EEG signal, represented by \(x\in\mathbb{R}^{\mathbb{C}\times\mathbb{T}}\), which includes data from C channels recorded over T time stamps, i.e.,\[x=\begin{bmatrix}x_{1}(t_{1})&x_{1}(t_{2})&\cdots&x_{1}(t_{7})\\ x_{2}(t_{1})&x_{2}(t_{2})&\cdots&x_{2}(t_{7})\\ \vdots&\vdots&&\vdots\\ x_{C}(t_{1})&x_{C}(t_{2})&\cdots&x_{C}(t_{7})\end{bmatrix} \tag{1}\]  
The goal is to predict whether an EEG segment indicates 'healthy control' or'sxiophrenia'. This is done by creating a function \(f\), parameterized by \(\theta\), that assigns a label \(\ell\) to each EEG segment. In the traditional approach, \(f\) is designed as a composition function (\(f_{3}\odot f_{2}\odot f_{1}\)) (\(x\)) = \(\ell\) where the functions \(f_{1},f_{2}\), and \(f_{3}\) are preprocessing of \(x\), feature extractor, and the classifier, respectively. A deep learning-based method learns the functions \(f_{1},f_{2}\), and \(f_{3}\) from the training data in an automatic way (i.e., without the need for human experts as done in hand engineering techniques). Deep learning can learn the hierarchical representation of the features by deriving low-level features from the input and high-level features from low-level ones [28; 29]. As such, we employed deep learning to formulate \(f\).  
Deep learning-based methods usually involve high parameter complexity. To keep the learnable parameter complexity small, we used an ensemble-like approach to design \(f\) for schizophrenia detection. The system design for \(f\) is shown in Figure 1; it takes an EEG trial \(x\) of six seconds temporal length as input, segments it into three frames \(\{\text{S}_{1},\text{S}_{2},\text{S}_{3}\}\), predicts the label of each frame after passing them to the 1D-CNN model, and finally takes the decision based on the majority vote. Splitting the input trial into smaller segments allows the design of a lightweight CNN model for scanning each segment, thereby reducing the complexity of the method. The main component of the system is the backbone 1D-CNN model, which is described in Section 3.2.  
This approach has three obvious benefits: (i) first, it does not use different base models to predict the label of an EEG trial; rather, it splits the EEG trial into three segments and passes each segment into the same backbone model to predict its label and final decision. The diversity comes from the split of EEG trial, avoiding the training of different deep models; (ii) second, it helps to keep the parameter complexity of the 1D-CNN model,  
Figure 1: The design of the system for schizophrenia detection. A six-second EEG trial is divided into three-second windows that are passed to 1D-CNN to predict their labels, which are finally fused to get the predicted label of the input trial.  
avoiding the overfitting problem, the parameter complexity of the model increases with the size of the input EEG trial, and the split of EEG trial helps to keep the parameter complexity smaller and provides a bigger number of training instances for better generalization of the backbone model; and (iii) third, it scales well to an EEG trial of any temporal length.