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The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas produces a new method for ranking a set of items. The essence of our idea is that a rank aggregation describes a partially filled skew-symmetric matrix. We extend an algorithm for matrix completion to handle skew-symmetric data and use that to extract ranks for each item. Our algorithm applies to both pairwise comparison and rating data. Because it is based on matrix completion, it is robust to both noise and incomplete data. We show a formal recovery result for the noiseless case and present a detailed study of the algorithm on synthetic data and Netflix ratings.
This work investigates the geometry of a nonconvex reformulation of minimizing a general convex loss function $f(X)$ regularized by the matrix nuclear norm $|X|_*$. Nuclear-norm regularized matrix inverse problems are at the heart of many application
In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal multi-rank
Rank minimization methods have attracted considerable interest in various areas, such as computer vision and machine learning. The most representative work is nuclear norm minimization (NNM), which can recover the matrix rank exactly under some restr
Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is NP-HARD,
Tensor nuclear norm (TNN) induced by tensor singular value decomposition plays an important role in hyperspectral image (HSI) restoration tasks. In this letter, we first consider three inconspicuous but crucial phenomenons in TNN. In the Fourier tran