## 3 Materials and Methods
### Proposed Model (HRIDM)
\(\gamma\) and \(\beta\) are the scaling and shifting parameters, \(\mu_{\text{B}}\) and \(\sigma_{\text{B}}\) are the batch mean and standard deviation. \(\alpha\) is the leakiness factor (0.01 in this case). The convolutional layer sizes for each stack are 128, 128, and 256, respectively, with a kernel size of \(1\times 1\), as shown by Equations (7)-(9) for each stack, respectively. (1) First Stack: \[Y_{stack1}=\text{max}\bigg{(}\alpha\cdot\bigg{(}\gamma_{1}\bigg{(}\frac{\sigma (W_{1}\times X+b_{1})-\mu_{\text{B1}}}{\sigma_{\text{B1}}}\bigg{)}+\beta_{1} \bigg{)},\gamma_{1}\bigg{(}\frac{\sigma(W_{1}\times X+b_{1})-\mu_{\text{B1}}}{ \sigma_{\text{B1}}}\bigg{)}+\beta_{1}\bigg{)}\] (7) Second Stack: \[Y_{stack2}=max\bigg{(}\alpha\cdot\bigg{(}\gamma_{2}\bigg{(}\frac{\sigma(W_{2} \times Y_{1}+b_{2})-\mu_{B2}}{\sigma_{\text{B2}}}\bigg{)}+\beta_{2}\bigg{)}, \gamma_{2}\bigg{(}\frac{\sigma(W_{2}\times Y_{1}+b_{2})-\mu_{B2}}{\sigma_{B2} }\bigg{)}+\beta_{2}\bigg{)}\] (8) Third Stack: \[Y_{stack3}=max\bigg{(}\alpha\cdot\bigg{(}\gamma_{3}\bigg{(}\frac{\sigma(W_{3} \times Y_{2}+b_{3})-\mu_{B3}}{\sigma_{B3}}\bigg{)}+\beta_{3}\bigg{)},\gamma_{3 }\bigg{(}\frac{\sigma(W_{3}\times Y_{2}+b_{3})-\mu_{B3}}{\sigma_{B3}}\bigg{)} +\beta_{3}\bigg{)}\] (9) To maintain weight preservation, an additional convolutional layer with 256 filters and batch normalization is incorporated into the skip connection, linking it with the output of the third stack in the residual block, which is shown by Equations (10) and (11): \[\text{skip}=\text{Conv1D}_{256}(X)\] (10) \[F(X)=Y_{stack3}+\text{Conv1D}_{256}(X)\] (11)
* _Inception block:_ This block is used to extract further low-dimensional features. The inception block involves stacks of 1D convolutional layers, followed by batch normalization and Leaky ReLU activation with an alpha value of \(1\times 10^{-2}\). Each stack utilizes 64 filters, with kernel sizes of 1, 3, and 5. (4) Kernel Size 1: \[\text{Output}[i]=\text{max}(\text{Input}[j\times\text{stride}:(j\times\text{ stride})+\text{pool\_size}-1])\]0 (12)(5) Kernel Size 3: \[\text{Output}[i]=\text{max}(\text{Input}[j\times\text{stride}:(j\times\text{ stride})+\text{pool\_size}-1])\]1 (13) (6) Kernel Size 5: \[\text{Output}[i]=\text{max}(\text{Input}[j\times\text{stride}:(j\times\text{ stride})+\text{pool\_size}-1])\]2 (14)  
Equations (12)-(14) illustrate how each stack within the inception block handles the input data \((X)\). The max operation integrates the Leaky ReLU output with a scaled and shifted variant to ensure non-linearity and extraction of features across various receptive fields (kernel sizes). The second and third sections contain almost identical layers, a repetitive structure of convolution, batch normalization, and Leaky ReLU to progressively extract increasingly detailed and refined features. The second section combines by concatenating the extracted features from its blocks with those from the first section. The third section follows a similar set of layers but incorporates skip connections to facilitate the flow of information across layers. * _Convolutional blocks:_ These blocks are used to capture complex patterns within the data. Each convolutional block consists of a 1D-Conv layer, batchNorm, and Leaky ReLU activation with an alpha value of \(1\times 10^{-2}\). The first convolutional block uses 128 filters, a filter size of \(5\times 5\), and a stride of \(1\times 1\), complemented by instance normalization and parametric ReLU activation. A dropout layer with a rate of 20% and a 1D max-pooling layer with a filter size of \(2\times 2\) was added. The second convolutional block is similar to the first, except for the filter count in the convolutional layer. It employs 256 filters of size \(11\times 11\) and the third convolutional block omits the 1D pooling layer and utilizes a Conv layer with 512 filters of size \(21\times 21\);
* _1D global average pooling (Global Avg. Pool) layer:_ This layer is utilized mainly for reducing the dimensionality of the feature data, presented by Equation (15).