Related papers: Top-N Recommendation with Novel Rank Approximation
In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…
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…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
Low rank matrix recovery is the focus of many applications, but it is a NP-hard problem. A popular way to deal with this problem is to solve its convex relaxation, the nuclear norm regularized minimization problem (NRM), which includes…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…
Recht, Fazel, and Parrilo provided an analogy between rank minimization and $\ell_0$-norm minimization. Subject to the rank-restricted isometry property, nuclear norm minimization is a guaranteed algorithm for rank minimization. The…
In recent years rank aggregation has received significant attention from the machine learning community. The goal of such a problem is to combine the (partially revealed) preferences over objects of a large population into a single,…
Low-rank decomposition plays a central role in accelerating convolutional neural network (CNN), and the rank of decomposed kernel-tensor is a key parameter that determines the complexity and accuracy of a neural network. In this paper, we…
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…
Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
PhaseLift, proposed by E.J. Cand\`{e}s et al., is one convex relaxation approach for phase retrieval. The relaxation enlarges the solution set from rank one matrices to positive semidefinite matrices. In this paper, a relaxation is employed…
Top-N recommendation aims to recommend each consumer a small set of N items from a large collection of items, and its accuracy is one of the most common indexes to evaluate the performance of a recommendation system. While a large number of…
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…
We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of…
Recommender systems are frequently used in domains in which users express their preferences in the form of graded judgments, such as ratings. If accurate top-N recommendation lists are to be produced for such graded relevance domains, it is…
Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the…
Research on recommender systems algorithms, like other areas of applied machine learning, is largely dominated by efforts to improve the state-of-the-art, typically in terms of accuracy measures. Several recent research works however…
Learning-to-Rank (LTR) is a supervised machine learning approach that constructs models specifically designed to order a set of items or documents based on their relevance or importance to a given query or context. Despite significant…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…