Related papers: Top-N Recommender System via Matrix Completion

This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…

In this paper we consider the collaborative ranking setting: a pool of users each provides a small number of pairwise preferences between $d$ possible items; from these we need to predict preferences of the users for items they have not yet…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix…

When a user connects to the Internet to fulfill his needs, he often encounters a huge amount of related information. Recommender systems are the techniques for massively filtering information and offering the items that users find them…

Matrix factorization is a widely used approach for top-N recommendation and collaborative filtering. When implemented on implicit feedback data (such as clicks), a common heuristic is to upweight the observed interactions. This strategy has…

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…

Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed…

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

Recommender systems have become an indispensable component in online services during recent years. Effective recommendation is essential for improving the services of various online business applications. However, serious privacy concerns…

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…

In this paper we provide a latent-variable formulation and solution to the recommender system (RS) problem in terms of a fundamental property that any reasonable solution should be expected to satisfy. Specifically, we examine a novel…

Although Recommender Systems have been comprehensively studied in the past decade both in industry and academia, most of current recommender systems suffer from the following issues: 1) The data sparsity of the user-item matrix seriously…

Top-$N$ recommender systems have been extensively studied. However, the sparsity of user-item activities has not been well resolved. While many hybrid systems were proposed to address the cold-start problem, the profile information has not…

Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle…