Low-Rank Matrix Completion via QR-Based Retraction on Manifolds

نویسندگان

چکیده

Low-rank matrix completion aims to recover an unknown from a subset of observed entries. In this paper, we solve the problem via optimization manifold. Specially, apply QR factorization retraction during optimization. We devise two fast algorithms based on steepest gradient descent and conjugate descent, demonstrate their superiority over promising baseline with ratio at least 24%.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Low-Rank Matrix Completion

While datasets are frequently represented as matrices, real-word data is imperfect and entries are often missing. In many cases, the data are very sparse and the matrix must be filled in before any subsequent work can be done. This optimization problem, known as matrix completion, can be made well-defined by assuming the matrix to be low rank. The resulting rank-minimization problem is NP-hard,...

متن کامل

Low-Rank Matrix and Tensor Completion via Adaptive Sampling

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor) and consequently, our results hold even when the row space is highly coherent, in contrast with previous an...

متن کامل

Robust Photometric Stereo via Low-Rank Matrix Completion and Recovery

We present a new approach to robustly solve photometric stereo problems. We cast the problem of recovering surface normals from multiple lighting conditions as a problem of recovering a low-rank matrix with both missing entries and corrupted entries, which model all types of non-Lambertian effects such as shadows and specularities. Unlike previous approaches that use Least-Squares or heuristic ...

متن کامل

Orthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix ...

متن کامل

Low-Rank Matrix Completion by Riemannian Optimization

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a novel algorithm for matrix completion that minimizes the least square distance on the sampling set over the Riemannian manifold of fixed-rank matrices. The algorithm is an adaptation of classical non-linear conjugate gradients, developed within the framework o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematics

سال: 2023

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math11051155