# Multi-Label Extreme Learning Machine (MLELMs) for Bangla Regional Speech Recognition
## 2 Materials and Methods
### Proposed Model
#### 2.2.2 Stacked Deep Convolutional Auto-Encoder  
An autoencoder (AE) is an artificial neural network (ANN) with many hidden layers with fewer nodes than the input and the output is expected to have a similar number of inputs. Convolutional Neural Networks, on the other hand, consist of three parts; convolutional layers, pooling layers, and fully connected layers. This is in contrast to the AE structure, which has input, hidden, and output layers. The input and output layers have \(n\) nodes for \(S\) samples in the autoencoder, each with feature vector \(\mathbf{F}_{i}\) for \(i=1,\ldots,S\) and \(\mathbf{F}_{i}eR^{n}\). As opposed to feed forward networks, autoencoders operate unsupervised. An autoencoder output is, \(\mathbf{F}=f_{1},f_{2},f_{3},\ldots,f_{n}\). In the encoder portion \(n\)-dimensional input data is converted to \(n^{\prime}\)-dimension. Where \(n^{\prime}\) is smaller to \(n\), to compress the input data to smaller dimension. Later in the decoded part of autoencoder, the decoded features in the \(n^{\prime}\)-dimensional form is converted back to \(n\)-dimension, which is decompressing the decoded features for the output nodes. The encoder maps the input \(\mathbf{F}\) to a set of hidden nodes \(H=h_{1},h_{2},h_{3},\ldots,h_{n}\). The node \(h_{j}\) output is computed as \[h_{j}=\varphi(\sum_{i=1}^{n}w_{ij}f_{i}+b_{j}), \tag{1}\]  
where \(\varphi\) represents the transfer function in the encoder section, \(i\) starts from \(1\), \(w_{ij}\) is the weight between \(f_{i}\) and \(h_{j}\), and \(b_{j}\) stands for the bias.  
\[f_{k}^{\prime}=\varrho(\sum_{j=1}^{n^{\prime}}w_{jk}h_{j}+b_{k}^{\prime}). \tag{2}\]  
In the decoded position function maps the H from encoded representation to estimated \(\mathbf{F}^{\prime}\). Hence, the output of the node \(f_{k}^{\prime}\) for the \(k^{th}\) position is as stated in Equation (2). \(\varrho\) act as the transfer function in the decoded side, \(j\) begins from \(1\), \(w_{ij}\) is the weight connection value for the \(h_{j}\) and \(f_{k}^{\prime}\) nodes and \(b_{k}^{\prime}\) is the bias for the \(k^{th}\) node in the decoder. Similar to the multi-layer perceptron the weights are updated through the iterative training of the AE through backpropagation.  
In the encoder section, convolutional layers with ReLU activation functions are followed by max pooling layers. In the encoder part, nonlinear transforms are used to map the input vector to the hidden representation. Next, the reverse transform is reconstructed from the hidden representation to the original audio input signal in the decoded part  
Figure 2: The architecture of Proposed Method consists of two parts. (**a**) SCAE (**b**) MLELMs.  
of the model. SCAE architecture is formed by using the reverse transform as the new representation of the input sample for another convolutional autoencoder, etc. Stacked Autoencoders (SAE) work similarly. For both encoded and decoded parts of the model, all the structures are kept symmetrical to identify low-dimensional hierarchical features in the data.  
A convolutional layer is applied in the bottleneck position to obtain a vector by flattening all the units and passing it to an embedded layer that is a low-dimensional, fully connected unit. This resulted in the 2D input data being transformed into lower dimensional features. Later, the multi-label extreme learning machines use the feature vector. The parameters of the decoder and encoder were updated to reduce re-construction error. Table 2. provides the architecture of SCAE.