*4.2. Nonlinear Techniques*

• Kernel PCA (KPCA) [28]: is an improved method of PCA, which uses kernel method techniques. KPCA computes the Eigenfaces or the Eigenvectors of the kernel matrix, while PCA computes the covariance matrix. In addition, KPCA is a representation of the PCA technique on the high-dimensional feature space mapped by the associated kernel function. Three significant steps of the KPCA algorithm are used to calculates the function of the kernel matrix K of distribution consisting of n data points xi ∈ Rd, after which the data points are mapped into a high-dimensional feature space F, as shown in Algorithm 2.

The performance of the KPCA technique depends on the choice of the kernel matrix K. The Gaussian or polynomial kernel are linear typically-used kernels. KPCA has been successfully used for novelty detection [72] or for speech recognition [62].

• Kernel linear discriminant analysis (KDA) [73]: the KLDA technique is a kernel extension of the linear LDA technique, in the same kernel extension of PCA. Arashloo et al. [73] proposed a nonlinear binary class-specific kernel discriminant analysis classifier (CS-KDA) based on the spectral regression kernel discriminant analysis. Other nonlinear techniques have also been used in the context of facial recognition:

