A fast adaptive randomized PCA algorithm

It is desirable to adaptively determine the number of dimensions (rank) for PCA according to a given tolerance of low-rank approximation error. In this work, we aim to develop a fast algorithm solving this adaptive PCA problem. We propose to replace the QR factorization in randQB_EI algorithm with matrix multiplication and inversion of small matrices, and propose a new error indicator to incrementally evaluate approximation error in Frobenius norm. Combining the shifted power iteration technique for better accuracy, we finally build up an algorithm named farPCA . Experimental results show that farPCA is much faster than the baseline methods (randQB_EI, randUBV and svds) in practical setting of multi-thread computing, while producing nearly optimal results of adpative PCA.