# Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method
## 5 Conclusions and Future Research  
In this study, the performance of several well-known pattern recognition strategies was analyzed to clarify which techniques are best suited to be applied in face recognition. We also analyzed the weakness and robustness of each technique. As already mentioned, DNE cannot correctly preserve local information of data because it only assigns +1 to intra-class and \(-1\) to inter-class neighbors, so it might fail to discover the most significant submanifolds for pattern classification. LPP is designed based on \"locality\" since it has no direct connection with classification, and it still suffers from the \"over learning of locality\" problem. LDNE has been proposed to overcome the problems existing in LPP and  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **S**KLDNE** & **LDNE** & **DNE** & **KPCA** & **LDA** & **LPP** & **UDP** & **PCA** \\ \hline Time (s) & 0.35 & 0.4 & 0.37 & 0.012 & 0.04 & 0.36 & 0.06 & 0.02 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The computational costs of the different classification methods using the Yale data base.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **16 \(\times\) 16** & **32 \(\times\) 32** & **64 \(\times\) 64** \\ \hline MLP & 64.76 & 84.76 & 86.19 \\ \hline DBNs + MLP & 88.57 & 89.05 & 90.95 \\ \hline SKLDNE & **100** & **100** & **100** \\ \hline \hline \end{tabular}
\end{table}
Table 8: Maximum recognition accuracies (in percentage terms) of SKLDNE and other methods on the JAFFE database.  
DNE; however, it does not guarantee an appropriate projection for classification purposes because many important non-linear data might be lost during its dimensionality reduction process. In addition, in some cases, LDNE cannot distinguish inter-class and intra-class neighbors well either in order to conduct projection for all points. This can degrade the classification performance. In order to address these problems, we have proposed a new supervised subspace learning algorithm named \"supervised kernel locality-based discriminant neighborhood embedding\" (SKLDNE). Combined with nonlinear data structures, locality, and discrimination information, SKLDNE can yield an optimal subspace that best finds the indispensable submanifolds-based structure. Six publicly available datasets, i.e., Yale face, ORL face, Sheffield, Head Pose, Finger Vein and Finger Knuckle, were used to illustrate the significance of the proposed technique. Experimental results reveal that SKLDNE outperforms and demonstrates potential to be implemented in real world systems compared to other advanced dimensionality reduction methods by obtaining the highest recognition rates in all experiments. Representing complex nonlinear variations makes SKLDNE more powerful and more intuitive than LDNE and other aforementioned techniques in terms of classification. According to the results, SKLDNE could also resolve the \"small training sample size\" problem, and it had the best performance compared to others at smaller numbers of projected dimensions in each number of training samples per data set. Moreover, when the given training sample size for each class grew larger, SKLDNE also achieved much better results than other techniques. The overlearning of locality problem and the out-of-sample problem in manifold learning can be avoided by applying our developed classifier. As a future plan, we will modify this classifier in order to make it directly applicable for two-dimensional data to effectively reduce the computational costs.  
Conceptualization, Methodology and Software, A.K.M.; Data and Formal Analysis, A.K.M. and J.J.C.A.; Resources, A.K.M., J.A.C.C. and J.J.C.A.; Writing--Original Draft Preparation, A.K.M.; Writing--Review & Editing, A.K.M., J.A.C.C. and J.J.C.A., Visualization, A.K.M.; Supervision, J.A.C.C. and J.J.C.A.; Project Administration, J.A.C.C. and J.J.C.A.; Funding Acquisition, J.A.C.C. and J.J.C.A. The APC was funded by the University of Malaga. The authors declare no conflict of interest.