Low-rank Approximation of Linear Maps
This work addresses a foundational mathematical problem in machine learning, offering theoretical tools for designing tractable algorithms in areas like kernel or continuous DMD.
The paper tackles the problem of low-rank approximation for bounded linear operators in Hilbert spaces, providing closed-form solutions and minimum achievable errors that generalize previous finite-dimensional results.
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results obtained in the finite dimensional case for the Frobenius norm. The theorem provides the basis for the design of tractable algorithms for kernel or continuous DMD.