PCA without eigenvalue calculations: a case study on face recognition*

Abstract Principal component analysis (PCA) is an extensively used dimensionality reduction technique, with important applications in many fields such as pattern recognition, computer vision and statistics. It employs the eigenvectors of the covariance matrix of the data to project it on a lower dimensional subspace. However, the requirement of PCA eigenvectors is a computational bottleneck which poses serious challenges and limits the applicability of PCA-based methods, especially for real-time computations. This paper proposes an alternative framework, relying on polynomial filtering which enables efficient implementations of PCA. We showcase the applicability of the proposed scheme on face recognition. In particular, we consider the eigenfaces methods which employ PCA. The numerical experiments reported indicate that the proposed technique competes with the PCA-based method in terms of recognition rate, while being much more efficient in terms of computational and storage cost.