Using a PCA algorithm to detect a specific person (test image.jpg) from a pool of faces (in training folder).
The algorithm is described in ‘Eigenfaces for Recognition’ by M. Turk and A. Pentland and it can be summarized as follows:

-calculate the average image $$Av=\Sum_{i=0}^{M}P_i$$ where $P_i$ is the photo $i$, $M$ is the number of images
-calculate the difference with the $D_i=P_i-Av$ $i\in 1,…M$
-calculate the eingenvectors $v_l$ of the transpose covariance matrix $L_{ij}=P_i^T P_j$
-determine the eigenvectors of the covariance matrix $C=L^T,\; u_l =\Sum_{i=0}^{M} v_{li}D_i$
-project the images to the reduced space ($l$ refers to the image and $k$ to the component) $imred_{lk} = u_k^T D_l$ $l,k\in 1,…M$
-project the test image to reduced space (Ptest refers to the test image $k$ index refers to the component) $ured_k = u_k^T ( Ptest-Av)$
-calculate the distance of the reduced vector ured with the images $||ured-imred_i||$ $i\in 1,..M$
-the minimum distance corresponds to the identified person