## 3 Materials and Methods
### Proposed Model (HRIDM)  
The aim of this research was to determine the most effective algorithm on the utilized dataset. Figure 5 depicts the proposed model and comprehensive methodology employed. The proposed HRIDM consists of three main sections. The first section serves as the input layer, incorporating multiple convolutional, residual, and inception blocks to extract the primary and fine features from the data, and is also responsible for producing output. We integrated residual blocks with inception blocks in our proposed model because this combination leverages the strength of both types of blocks, enhancing the overall performance of the model for arrhythmia detection in 12-lead ECG recordings. The residual blocks address the problem of vanishing gradient problem and perform deeper training through skip connections which allows the models to learn complex features in an effective manner whereas the inception blocks capture the multiscale fine and detail features because of the parallel Conv blocks with varying filter sizes. The fusion of both techniques provides the powerful structure of the DL model, enabling it to efficiently and effectively learn the diverse features and enhancing its ability to discriminate between different arrhythmia types, resulting in improved accuracy and robustness compared to other models. The second section is connected with the first and further refines the extracted features, subsequently concatenating them. The third section is connected with both preceding sections (first and second) and combines the concatenated features. The output of the final section is given to the dense layer of the first section to produce the desired output. A detailed description of each section and its constituent blocks follows. The first section of the proposed model consists of the following layers:  
The proposed model is a deep learning model that consists of the following layers:  
* _1D convolutional (Conv) layers:_ In our proposed model, we have utilized multiple 1D-Convolution (Conv) layers for extracting high level features from the provided dataset. The first 1D-Conv layer employs 512 kernels, each of size 5 \(\times\) 5, to learn informative patterns from the input data. The second 1D-Conv layer includes 256 kernels of size 3 \(\times\) 3, further refining the extracted features. Following each 1D-Conv layer, we incorporate batch normalization (batchNorm) to improve training stability and accelerate convergence. Further, ReLU activation functions are included to introduce non-linearity and improve the model's ability to learn complex relationships within the data. The convolutional layer computes the output Output\([i,j,k]\) at spatial position \((i,j)\) and output channel \(k\) as given in Equation (2): \[\text{Output}[i,j,k]=\sum_{f,g,h}(\text{Filter}[f,g,h]\times\text{Input}[i+f,j +g,h])+\text{Bias}[k]\] (2)* _1D max-pooling (MaxPool) layer:_ This layer is utilized to downsample the data while preserving prominent features. The 1D-maxPool layer employs a 3 \(\times\) 3 size filter with stride 2, and it computes the output Output\([i]\) at position \(i\) as given in Equation (3): \[\text{Output}[i]=\text{max}(\text{Input}[j\times\text{stride}:(j\times\text{ stride})+\text{pool\_size}-1])\] (3)
* _Residual block:_ This block is used to address the vanishing gradient problem and facilitate weight transfer. The residual block consists of three stacks, each comprising a 1D-Conv layer, batchNorm, and Leaky ReLU activation function with an alpha value of \(1\times 10^{-2}\), which are given by Equations (4)-(6), respectively: \[Y_{\text{conv}}=\sigma(W\times X+b)\] (4) \[Y_{\text{bn}}=\gamma\bigg{(}\frac{Y_{\text{conv}}-\mu_{\text{B}}}{\sigma_{ \text{B}}}\bigg{)}+\beta\] (5) \[Y_{\text{out}}=\text{max}(\alpha\cdot Y_{\text{bn}},Y_{\text{bn}})\] (6) where \(W\) is the filter weights, \(X\) is the input data, \(b\) is the bias term, and \(\sigma\) is the activation function (Leaky ReLU).