## 4 Proposed Work
The features which were highly correlated with the class were considered to be relevant and the features those were highly correlated with each other were considered to be redundant. The calculation of PCC is performed using Equation (13),

Figure 5: Diagrammatic representation of the feature selection process using supervised filter harmony search algorithm (SFHSA). where \(x\) and \(y\) were two sets of values and \(\overline{x}\) and \(\overline{y}\) are their expectation values respectively. The values of both \(R\) and \(D\) were calculated using Equations (14) and (15) respectively. \(x_{i}\) and \(x_{j}\) represent features from the feature subset \(S\) and \(c\) represents the facial class label. \[PCC(x,y)=\frac{\sum(x-\overline{x})(y-\overline{y})}{\sqrt{\sum(x-\overline{x })^{2}(y-\overline{y})^{2}}} \tag{13}\]

\[R=\frac{1}{|S|}\sum_{x_{i}\in S}PCC(x_{i},c) \tag{14}\]

\[D=\frac{1}{|S^{2}|}\sum_{x_{i},\ x_{j}\in S}PCC\Big{(}x_{i},x_{j}\Big{)} \tag{15}\]

The value of mRMR is calculated based on finding out the quality score of the feature subset defined by \(V(S)\), defined in Equation (16) as follows:

\[V(S)=R-D \tag{16}\]

During the decision-making process, if the quality score of the newly generated feature subset is found to be better than the worst subset in HM, it replaces the worst subset and again the worst subset is found out from the updated HM. The entire process is iterated until the stopping criterion is met. The finishing stage of the process includes calculating the accuracy score using a classifier and generating the results which is discussed in the next section. Therefore, the proposed HSA is a filter-based FS method based on mRMR. The use of PCC in mRMR makes the algorithm quite effective in selecting the best subsets. The extracted feature descriptors were refined using SFHSA, and the final selected features were chosen from the testing feature sets and passed through a classifier to find the recognition accuracy of the classification problem under consideration (here, FER). A schematic diagram of the proposed model is shown in Figure 6.

Figure 6: Schematic diagram of the proposed feature selection model called SFHSA developed for classification of facial emotions. ## 5 Results and Discussion

The SFHSA-based FS technique was applied to the features obtained from the images of two standard FER datasets, namely JAFFE and RaFD. The five feature sets obtained include uLBP, hvnLBP, Gabor-filter-based, HOG, PHOG features. We considered the facial images of three dimensions: \(32\times 32,\ 48\times 48\) and \(64\times 64\). As a result, for the present FS problem, the total number of feature sets taken under consideration becomes 30 (\(=2\times 5\times 3\) ), 2 FER datasets, 5 feature sets and facial images of 3 dimensions. Table 2 represents the measurement of sizes of the 5 feature vectors produced using 3 different dimensions of the facial images along with its recognition accuracy. This table also highlights the size of reduced-feature vector with recognition accuracy from two standard FER datasets. As mentioned previously, each feature set was segregated into training and testing sets with ratio of 2:1 and SFHSA was applied on the training set only. The testing set was used to get the accuracy score by only selecting the attributes (feature indices) that were present in the reduced version of training feature set, defined as follows:

\[Accuracy\ score(\%)=\frac{\#facial\ images\ successfully\ recognized}{\#total\ facial\ images\ in\ the\ test\ set}\times 100 \tag{17}\]