## 4 Methodology
### Fine Classification  
A CNN has been optimised based on the AdaBoost [55] technique for each coarse class estimated by natural distribution. A sequential linear CNN boosting has been performed to obtain the classification results where a block level abstraction of coarse, fine, and final classification is presented in Figure 4.  
Considering each coarse class as a combination of multiple classes, a multi-class classification problem can be defined as:  
\[\widehat{c}=\arg\max_{\theta\in\{1...k\}}h_{\theta}(x), \tag{6}\]  
where \(x\) is an unseen element of data randomly sampled from \(k\) classes. The classifier \(h_{\theta}\) is trained on dataset \(T=\{t_{1},t_{2},t_{3},\ldots,t_{n}\}\) to assign a label \(\widehat{c}\) to \(x\) such that the corresponding classification error is minimum. In our proposed approach, we have used the multi-class AdaBoost technique defined in [56] to optimise a CNN for each coarse class. The elements in the training dataset of each coarse class are initially weighted equally as: \(s_{ti}=1/n\) where \(n\) is the size of the training dataset. The CNN is then trained on \(T\) for \(J\) iterations to obtain an optimised CNN, where ImageNet weights have been used for the initialisation of the CNN when \(J=0\). The dataset weights of each element \(t_{i}\) are updated after each iteration for \(J\geq 1\). The corresponding weight of each \(t_{i}\) is estimated by extracting a \(k\) dimensional classification likelihood vector with a trained classifier (i.e., CNN) \(h_{\theta}^{j\geq 1}\). This \(k\) dimensional vector \(\mathcal{P}\) is used for the estimation of weight for each \(t_{i}\) in \(T\) after every iteration, which can be described as:  
\[s_{ti}^{j}=s_{ti}^{j-1}\,exp\Big{(}-\alpha\,\frac{k-1}{k}\,\,\xi_{g}^{i}\,\log (\mathcal{P}^{j}(t_{i}^{j-1}))\Big{)}, \tag{7}\]  
where \(s_{ti}\) is the weight of \(i\)th training sample in \(T\) used in the \(j\)th iteration with a learning rate of \(\alpha\). The ground truth labels of corresponding classes are represented as \(\widehat{c}_{g}^{i}\) for \(k\) dimensional likelihood vectors. The weights of the wrongly classified samples are improved in each iteration to optimise the classifier for wrongly classified samples in \(j-1\)th iterations. The AdaBoost [56] uses a random forest as a combination of trees to make an ensemble of weak learners where, each contributing tree is initialised with random weights. The CNNs have the capability of finding a strong classification likelihood and correlations for a large dataset. However, considering the findings in (7) it can be concluded that strong correlation between \(\widehat{c}_{g}^{i}\) and the output of the CNN will reduce the value of the exponential function, which will constrain the weights improvement to a small set of data not trained with the CNN previously. Training the CNNs on a small dataset can cause significant overfitting, and will add an overhead of extra computational cost. We initialised the CNN with the ImageNet weights for the first iteration where the weights of the CNN in further optimisation iterations have been retained and improved with the weighted training samples. This assumption has been made considering the sequential Representation Learning (RL) of a CNN in the training process, where retaining the previous information can help in the effective convergence of the CNN for a large dataset. This iterative process is repeated for all coarse classes obtained in the initial stage of the classification process. A detailed process for the fine classification stage has been described in Figure 4.  
The CNNs used in the fine classification stage are a combination of a number of layers stacked together to perform the classification task. Each layer in the CNN plays a specific role for RL where the level of abstraction of the features learned increases from lower to upper layers. The low-level features i.e., pixel-level textures, are extracted with the help of conventional layers. These features are then combined in a Fully Connected (FC) layer.