Abstract
In this paper, we study low-rank matrix nearness problems, with a focus on learning low-rank positive semidefinite (kernel) matrices for machine learning applications. We propose efficient algorithms that scale linearly in the number of data points and quadratically in the rank of the input matrix. Existing algorithms for learning kernel matrices often scale poorly, with running times that are cubic in the number of data points. We employ Bregman matrix divergences as the measures of nearness---these divergences are natural for learning low-rank kernels since they preserve rank as well as positive semidefiniteness. Special cases of our framework yield faster algorithms for various existing learning problems, and experimental results demonstrate that our algorithms can effectively learn both low-rank and full-rank kernel matrices.
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.