论文标题
鲁棒正交张量近似的乘数的半季度交替方向方法
Half-Quadratic Alternating Direction Method of Multipliers for Robust Orthogonal Tensor Approximation
论文作者
论文摘要
近年来，已经对具有一个或多个潜在因子矩阵的高阶规范多核分解（CPD）进行了很好的研究。但是，大多数现有模型通过使用最小二乘损失来惩罚噪音（如果发生），这可能对非高斯噪声或异常值敏感，从而导致对潜在因素的偏见估计。在本文中，基于最大后验估计，我们得出了具有cauchy损失的强大正交张量CPD模型，该模型对重尾噪声或异常值有抵抗力。通过探索模型的半季度特性，提出了一种新方法，该方法被称为乘数的半季度交替方向方法（HQ-ADMM）来解决模型。 HQ-ADMM中涉及的每个子问题都允许封闭式解决方案。得益于库奇损失的一些不错的特性，我们表明，全球算法生成的整个序列将整个序列收敛到所考虑的问题的固定点。关于合成和实际数据的数值实验证明了所提出的模型和算法的效率和鲁棒性。
Higher-order tensor canonical polyadic decomposition (CPD) with one or more of the latent factor matrices being columnwisely orthonormal has been well studied in recent years. However, most existing models penalize the noises, if occurring, by employing the least squares loss, which may be sensitive to non-Gaussian noise or outliers, leading to bias estimates of the latent factors. In this paper, based on the maximum a posterior estimation, we derive a robust orthogonal tensor CPD model with Cauchy loss, which is resistant to heavy-tailed noise or outliers. By exploring the half-quadratic property of the model, a new method, which is termed as half-quadratic alternating direction method of multipliers (HQ-ADMM), is proposed to solve the model. Each subproblem involved in HQ-ADMM admits a closed-form solution. Thanks to some nice properties of the Cauchy loss, we show that the whole sequence generated by the algorithm globally converges to a stationary point of the problem under consideration. Numerical experiments on synthetic and real data demonstrate the efficiency and robustness of the proposed model and algorithm.
