A novel local extrema based gravitational search algorithm and its application in face recognition using one training image per class

In this present paper a new methodology has been presented involving a stochastic optimization based approach to solve the face recognition problem with only one training image per class. Singular value decomposition (SVD) is used to decompose the single training image into two component images in order to compute the within class scatter matrix. The stochastic optimization approach is implemented employing gravitational search algorithm (GSA) which searches for an optimal transform matrix instead of using the traditional solution of general eigenvalue problem as is carried out in Fisher linear discriminant analysis (FLDA). The present paper also proposes two novel variants of GSA, namely the 2-D version of GSA, in order to cater for the 2-D image data, and the other one is a 2-D randomized local extrema based GSA (RLEGSA), which employs a stochastic local neighborhood based search instead of global search, as in basic GSA. Finally, a novel concept of performing an automated selection of projection vectors is incorporated in the 2-D RLEGSA to propose an improved variant, called the Modified RLEGSA (MRLEGSA). Experimental results, based on benchmark Yale A and ORL databases, show that the proposed methods outperform several existing schemes.