# Facial Expression Recognition Based on Discrete Separable Shearlet Transform and Feature Selection
## 4 Results and Discussion
### Contrast Experiment  
Table 3 compares the proposed FER method with state-of-the-art methods, which were selected because they use frequency domain features, a similar testing strategy, and the same dataset. For a fair comparison, we implemented some of these methods, and for those which we did not, we quoted their published results. A 10-fold cross-validation scheme was used on each dataset. For the four datasets, the weighted average recognition rates of the state-of-the-art methods and the proposed method are shown in Table 3. Table 3 clearly indicates that the proposed method outperforms the state-of-the-art methods for the four datasets. The weighted average recognition rate of the proposed method was 7.62%, 1.46%, 1.98%, 4.27%, 10.71%, and 6.25% higher than the rates of the methods proposed in [27; 28; 29; 30; 31; 32], respectively.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Data Set** & **Average Accuracy Rate (\%)** \\ \hline \multirow{4}{*}{With feature selection} & JAFFE & 98.00 \\  & CK+ & 95.17 \\  & MMI & 96.02 \\  & PICS & 97.33 \\ \hline \multirow{4}{*}{Without feature selection} & JAFFE & 94.06 \\  & CK+ & 91.50 \\ \cline{1-1}  & MMI & 92.23 \\ \cline{1-1}  & PICS & 92.50 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of average accuracy rate of the proposed method with and without feature selection on the four data sets.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Training Dataset.** & **Testing Datasets** & **Average Accuracy Rate (\%)** \\ \hline JAFFE & CK+, MMI, PICS & 87.89 \\ CK+ & JAFFE, MMI, PICS & 84.97 \\ MMI & JAFFE, CK+, PICS & 85.62 \\ PICS & JAFFE, CK+, MMI & 86.38 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average accuracy rate of the proposed method trained on one dataset and tested on the others.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Average Accuracy Rate/\%** \\ \hline Ref. [27] method & 89.01 \\ Ref. [28] method & 95.17 \\ Ref. [29] method & 94.65 \\ Ref. [30] method & 92.36 \\ Ref. [31] method & 85.92 \\ Ref. [32] method & 90.38 \\ Proposed method & 96.63 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the proposed method with state-of-the-art methods in terms of average accuracy rate.  
Moreover, the quantization algorithm has a complexity of \(O(M)\), and \(M\) is the number of features. The experiments were performed in MATLAB R2014a, [Intel-(R) Core-(TM) (3.60 GHz) with a RAM capacity of 56 GB]. The proposed framework has a complexity of \(O(TM)\), and \(T\) is the number of input expression images.  
In order to analyze the computational cost of the proposed framework, we selected the most efficient method (that is, [27] from the above experiments of Table 3). The framework of [27] took 1493 ms, 1998 ms, 1215 ms, and 2031 ms to recognize an expression frame from JAFFE, CK+, MMI, and PICS datasets of facial expressions, respectively. On the other hand, our framework took 1185 ms, 1826 ms, 1002 ms, and 1725 ms to recognize an expression frame from the same datasets. Thus, our framework not only achieved high recognition rate, but it is also less expensive in terms of computational.