# Multi-Label Extreme Learning Machine (MLELMs) for Bangla Regional Speech Recognition
## 2 Materials and Methods
### Proposed Model
#### 2.2.3 Extreme-Learning Machine (ELM)  
This is an efficient, compact and sophisticated single layer feed forward neural network that performs classification in a systematic and effective manner [33]. The MLELM architecture is composed of 3 layers: input, hidden, and output. Here the input samples are denoted as \(\mathbf{F}\) and \(\mathbf{F}\,\epsilon R^{n}\), class labels are represented as \(\mathbf{Y}\) where \(\mathbf{Y}\,\epsilon R^{E}\). The input layer have \(I\) number of nodes, hidden layers have \(D\) and output layers have \(E\) number of nodes. The weights for the input layer to hidden nodes are represented by \(\omega\), while the weights from hidden layer to output is denoted by \(\omega\)  
It is unlike most ANNs in that the weights associated with the input layer and the biases are randomly initialized and are not updated later. Only the hidden layer in the network learns from the data input, which is reflected in the hidden layer's weights. \(\theta\) is the activation function for the hidden nodes. \(h_{j}\) hidden node, output from the hidden layers are calculated as follows: \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Layer Names** & **Architecture** & **Feature Map Size** & **Parameters** \\ \hline Conv1 & 32 \(\times\) 128 \(\times\) 1 & 32 \(\times\) 64 \(\times\) 32 & 29 K \\ Maxpool & (Max 2 \(\times\) 2) & 32 \(\times\) 32 \(\times\) 32 & \\ Bottleneck-Conv & 32 \(\times\) 32 \(\times\) 32 & 8 \(\times\) 8 \(\times\) 16 & 768 K \\ Deconv1 & 8 \(\times\) 8 \(\times\) 16 & 32 \(\times\) 64 \(\times\) 32 & \\ unpool & Max (2 \(\times\) 2) & 32 \(\times\) 128 \(\times\) 1 & \\ \hline Conv1 & 32 \(\times\) 128 \(\times\) 1 & 32 \(\times\) 32 \(\times\) 64 & 228 K \\ Maxpool & (Max 2 \(\times\) 2) & 16 \(\times\) 16 \(\times\) 128 & \\ Conv2 & 16 \(\times\) 16 \(\times\) 128 & 8 \(\times\) 8 \(\times\) 256 & 12 K \\ Maxpool & (Max 2 \(\times\) 2) & 4 \(\times\) 4 \(\times\) 512 & \\ Bottleneck-Conv & 4 \(\times\) 4 \(\times\) 512 & 2 \(\times\) 2 \(\times\) 124 & 221 K \\ Deconv1 & 2 \(\times\) 2 \(\times\) 124 & 8 \(\times\) 8 \(\times\) 256 & \\ unpool & Max (2 \(\times\) 2) & 16 \(\times\) 16 \(\times\) 128 & \\ Deconv2 & 16 \(\times\) 16 \(\times\) 128 & 32 \(\times\) 32 \(\times\) 64 & \\ unpool & Max (2 \(\times\) 2) & 32 \(\times\) 128 \(\times\) 1 & \\ \hline Conv1 & 32 \(\times\) 128 \(\times\) 1 & 32 \(\times\) 64 \(\times\) 32 & 30 K \\ Maxpool & (Max 2 \(\times\) 2) & 32 \(\times\) 32 \(\times\) 64 & \\ Conv2 & 32 \(\times\) 32 \(\times\) 64 & 16 \(\times\) 16 \(\times\) 128 & 250 K \\ Maxpool & (Max 2 \(\times\) 2) & 8 \(\times\) 8 \(\times\) 128 & \\ Conv3 & 8 \(\times\) 8 \(\times\) 128 & 4 \(\times\) 4 \(\times\) 256 & 12 K \\ Maxpool & (Max 2 \(\times\) 2) & 4 \(\times\) 4 \(\times\) 512 & \\ Bottleneck-Conv1 & 4 \(\times\) 4 \(\times\) 512 & 4 \(\times\) 4 \(\times\) 256 & 885 K \\ Bottleneck-Conv2 & 4 \(\times\) 4 \(\times\) 256 & 2 \(\times\) 2 \(\times\) 124 & 885 K \\ Deconv1 & 2 \(\times\) 2 \(\times\) 124 & 4 \(\times\) 4 \(\times\) 256 & \\ unpool & Max (2 \(\times\) 2) & 8 \(\times\) 8 \(\times\) 128 & \\ Deconv2 & 8 \(\times\) 8 \(\times\) 128 & 16 \(\times\) 16 \(\times\) 128 & \\ unpool & Max (2 \(\times\) 2) & 32 \(\times\) 32 \(\times\) 64 & \\ Deconv3 & 32 \(\times\) 32 \(\times\) 64 & 32 \(\times\) 64 \(\times\) 32 & \\ unpool & Max (2 \(\times\) 2) & 32 \(\times\) 128 \(\times\) 1 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proposed method detailed architecture. \[h_{j}=\vartheta(\sum_{i=1}^{n}\omega_{ij}f_{i}+b_{j}), \tag{3}\]  
where, \(\omega_{ij}\) represents the connection weight between \(f_{i}\) and \(h_{j}\), and \(b_{j}\) is the bias. As a result the output node \(o_{k}\)  
\[o_{k}=\sum_{D}^{j=1}h_{j}\varpi_{jk}, \tag{4}\]  
\(\varpi_{jk}\) represent the weight between the \(h_{j}\) and \(o_{k}\). Once the MLELM model obtains the weight matrix of \(\varpi\), it is considered to have learned iteratively from the training phase.