Incremental Eigen Decomposition

Eigen decomposition is a central mathematical tool in many pattern recognition and machine learning techniques. However, it becomes computationally infeasible in the presence of a large set of high-dimensional samples. Moreover, in highly dynamic domains with a continual supply of new samples, an incremental approach that keeps on updating the eigen decomposition will be more desirable than the traditional approach of simply re-computing the decomposition from scratch. In this paper, by using a method for updating singular value decompositions, we propose a procedure to obtain an approximate eigen decomposition by processing the samples in chunks or sequentially. On applying this to principal component analysis for image denoising, experimental results show that this restricted form of updating can still achieve comparable performance as the batch version.