## 3 Methodology and Materials
### MI for Feature Selection  
_MI_ is a fundamental concept in information theory that plays a pivotal role in various fields, including scene recognition in computer vision. _MI_ quantifies the dependency between two random variables, providing a measure of the amount of information that knowing one variable provides about the other. In the context of scene recognition, _MI_ is a valuable tool for assessing the relationship between different image features or modalities, aiding in feature selection, fusion, and optimization processes. Mathematically, _MI_ between two discrete random variables \(X\) and \(Y\) is defined as [25]:  
\[MI(X;Y)=\sum_{x\in X}\sum_{y\in Y}p(x,y)log\left(\frac{p(x,y)}{p(x)p(y)}\right) \tag{1}\]  
where _MI_(\(X;Y\)) represents the _MI_ between \(X\) and \(Y\). _p_(\(x\),\(y\)) is the joint probability mass function of \(X\) and \(Y\). _p_(\(x\)) and _p_(\(y\)) are the marginal probability mass functions of \(X\) and \(Y\), respectively. In essence, _MI_ quantifies how much knowing one variable reduces the uncertainty about the other variable. If \(X\) and \(Y\) are independent, _MI_(\(X;Y\)) equals zero, as the knowledge of one variable provides no information about the other. Conversely, when \(X\) and \(Y\) are perfectly dependent, _MI_(\(X;Y\)) is maximized. In the context of scene recognition, _MI_ is utilized to assess the degree of dependency or correlation between image features or modalities. This evaluation is pivotal in several aspects of scene recognition:  
1. Feature Selection: _MI_ helps identify and select the most informative features or modalities for scene recognition. By calculating _MI_ between each feature (\(F\)) and the target scene label (\(L\)), less relevant or redundant features can be pruned, enhancing computational efficiency and reducing the risk of overfitting. The formula for this feature selection process is: \[MI(F,L)=\sum(f\in F)\sum(l\in L)p(f,l)*log\left[\frac{p(f,l)}{p(f)*p(l)}\right]\] (2) where \(\bullet\)\(MI(F,L)\) represents the _MI_ between the feature \(F\) and the scene label \(L\). \(\bullet\)\(p(f,l)\) is the joint probability mass function of the feature \(F\) and the scene label \(L\). \(\bullet\)\(p(f)\) and \(p(l)\) are the marginal probability mass functions of the feature \(F\) and the scene label \(L\), respectively. 2. Multimodal Fusion: In multimodal scene recognition, _MI_ quantifies the interdependence between different data modalities (e.g., text, audio, depth) and the scene labels (\(L\)). This assists in determining how to combine modalities effectively, such as weighing them based on their _MI_ with the scene label. The weighted fusion formula can be represented as: \[Weighted\ Fusion=W1*MI(M1,L)+W2*MI(M2,L)+\ldots\] (3) \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline Maximum Epochs & 30 \\ \hline Initial Learning Rate & 3.0000000 \(\times\) 10\({}^{-4}\) \\ \hline Learning Rate Schedule & Piecewise \\ \hline Learning Rate Drop Factor & 0.5 \\ \hline Learning Rate Drop Period & 5 \\ \hline Data Shuffling & Every Epoch \\ \hline Validation Frequency & 87 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._where  
* Weighted Fusion represents the combined information from multiple modalities. * _MI_(_Mi_,_L_) is the mutual information between each modality (_Mi_) and the scene label \(L\). * _w1_, _w2_, etc., are weights assigned to each modality, which can be determined based on their _MI_ values. * Optimization: _MI_ can be employed in optimization processes to improve feature representations. Genetic Algorithms, for example, can utilize _MI_ as an objective function, enhancing the discriminative power and robustness of features extracted from the same input image data. The objective function for optimization can be defined as: \[\textit{Objective Function}=MI(F1,L)+MI(F2,L)+\ldots+MI(Fn,L)\] (4) where
* _MI_(_Fi_,_L_) represents the mutual information between each feature (_Fi_) and the scene label \(L\). * \(n\) is the number of features under consideration.