Adaptive spectrum transformation by topology preserving on indefinite proximity data

Similarity-based representation generates indefinite matrices, which are inconsistent with classical kernel-based learning frameworks. In this paper, we present an adaptive spectrum transformation method that provides a positive semidefinite ( psd ) kernel consistent with the intrinsic geometry of proximity data. In the proposed method, an indefinite similarity matrix is rectified by maximizing the Euclidian fac- tor ( EF ) criterion, which represents the similarity of the resulting feature space to Euclidean space. This maximization is achieved by modifying volume elements through applying a conformal transform over the similarity matrix. We performed several experiments to evaluate the performance of the proposed method in comparison with flip, clip, shift , and square spectrum transformation techniques on similarity matrices. Applying the resulting psd matrices as kernels in dimensionality reduction and clustering problems confirms the success of the proposed approach in adapting to data and preserving its topological information. Our experiments show that in classification applications, the superiority of the proposed method is considerable when the negative eigenfraction of the similarity matrix is significant

State of the Art in Face Recognition

Notwithstanding the tremendous effort to solve the face recognition problem, it is not possible yet to design a face recognition system with a potential close to human performance. New computer vision and pattern recognition approaches need to be investigated. Even new knowledge and perspectives from different fields like, psychology and neuroscience must be incorporated into the current field of face recognition to design a robust face recognition system. Indeed, many more efforts are required to end up with a human like face recognition system. This book tries to make an effort to reduce the gap between the previous face recognition research state and the future state

A geometrical method to improve performance of the support vector machine

The performance of a support vector machine (SVM) largely depends on the kernel function used. This letter investigates a geometrical method to optimize the kernel function. The method is a modification of the one proposed by S. Amari and S. Wu. Its concern is the use of the prior knowledge obtained in a primary step training to conformally rescale the kernel function, so that the separation between the two classes of data is enlarged. The result is that the new algorithm works efficiently and overcomes the susceptibility of the original method