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Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real applications, such as image inpainting and recommender systems. Many existing approaches formulate this problem as a general low-rank matrix approximation problem. Since the rank operator is nonconvex and discontinuous, most of the recent theoretical(More)
Estimating missing values in visual data is a challenging problem in computer vision, which can be considered as a low rank matrix approximation problem. Most of the recent studies use the nuclear norm as a convex relaxation of the rank operator. However, by minimizing the nuclear norm, all the singular values are simultaneously minimized, and thus the rank(More)
Recently, hashing techniques have been widely applied to solve the approximate nearest neighbors search problem in many vision applications. Generally, these hashing approaches generate 2^c buckets, where c is the length of the hash code. A good hashing method should satisfy the following two requirements: 1) mapping the nearby data points into the same(More)
Cross media retrieval engines have gained massive popularity with rapid development of the Internet. Users may perform queries in a corpus consisting of audio, video, and textual information. To make such systems practically possible for large mount of multimedia data, two critical issues must be carefully considered: (a) reduce the storage as much as(More)
Nowadays, Nearest Neighbor Search becomes more and more important when facing the challenge of big data. Traditionally, to solve this problem , researchers mainly focus on building effective data structures such as hierarchical k-means tree or using hashing methods to accelerate the query process. In this paper, we propose a novel unified approximate(More)
In many real world scenarios, active learning methods are used to select the most informative points for labeling to reduce the expensive human action. One direction for active learning is selecting the most representative points, ie., selecting the points that other points can be approximated by linear combination of the selected points. However, these(More)
Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real world applications, such as recommender system and image in-painting. These problems can be formulated as a general matrix completion problem. The Singular Value Thresholding (SVT) algorithm is a simple and efficient first-order matrix completion(More)
Recently, the hashing techniques have been widely applied to approximate the nearest neighbor search problem in many real applications. The basic idea of these approaches is to generate binary codes for data points which can preserve the similarity between any two of them. Given a query, instead of performing a linear scan of the entire data base, the(More)