FLPI: An optimal algorithm for document indexing based on LPI

LPI is optimal in the sense of local manifold structure. However, LPI is not efficient in time and memory which makes it difficult to be applied to very large data set. In this paper, we propose a optimal algorithm called FLPI. FLPI decomposes the LPI problem as a graph embedding problem plus a regularized least squares problem. Such modification avoids eigen decomposition of dense matrices and can significantly reduce both time and memory cost in computation. Moreover, with a specifically designed graph in supervised situation, LPI only needs to solve the regularized least squares problem which is a further saving of time and memory. Real data experimental results show that FLPI obtains similar or better results comparing to LPI and it is significantly faster.