Reduced basis decomposition: A certified and fast lossy data compression algorithm

摘要

Dimension reduction is often needed in the area of data mining. The goal of these methods is to map the given high-dimensional data into a low-dimensional space preserving certain properties of the initial data. There are two kinds of techniques for this purpose. The first, projective methods, builds an explicit linear projection from the high-dimensional space to the low-dimensional one. On the other hand, the nonlinear methods utilizes nonlinear and implicit mapping between the two spaces. In both cases, the methods considered in literature have usually relied on computationally very intensive matrix factorizations, frequently the Singular Value Decomposition (SVD). The computational burden of SVD quickly renders these dimension reduction methods infeasible thanks to the ever-increasing sizes of the practical datasets.