Abstract
Dictionary learning is an important sparse representation algorithm which has been widely used in machine learning and artificial intelligence. However, for massive data in the big data era, classical dictionary learning algorithms are computationally expensive and even can be infeasible. To overcome this difficulty, we propose new dictionary learning methods based on randomized algorithms. The contributions of this work are as follows. First, we find that dictionary matrix is often numerically low-rank. Based on this property, we apply randomized singular value decomposition (RSVD) to the dictionary matrix, and propose a randomized algorithm for linear dictionary learning. Compared with the classical K-SVD algorithm, an advantage is that one can update all the elements of the dictionary matrix simultaneously. Second, to the best of our knowledge, there are few theoretical results on why one can solve the involved matrix computation problems inexactly in dictionary learning. To fill-in this gap, we show the rationality of this randomized algorithm with inexact solving, from a matrix perturbation analysis point of view. Third, based on the numerically low-rank property and Nyström approximation of the kernel matrix, we propose a randomized kernel dictionary learning algorithm, and establish the distance between the exact solution and the computed solution, to show the effectiveness of the proposed randomized kernel dictionary learning algorithm. Fourth, we propose an efficient scheme for the testing stage in kernel dictionary learning. By using this strategy, there is no need to form nor store kernel matrices explicitly both in the training and the testing stages. Comprehensive numerical experiments are performed on some real-world data sets. Numerical results demonstrate the rationality of our strategies, and show that the proposed algorithms are much efficient than some state-of-the-art dictionary learning algorithms. The MATLAB codes of the proposed algorithms are publicly available from https://github.com/Jiali-yang/RALDL_RAKDL.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.