基于加权Schatten-p范数的矩阵填充及其应用

MATRIX COMPLETION WITH WEIGHTED SCHATTEN-P NORM AND ITS APPLICATION

基于核范数的矩阵填充模型中,由于对所有奇异值的惩罚力度一样以及实际应用中核范数对秩函数的逼近效果不佳,导致评分矩阵填充时准确性不高。针对这种情况,提出一种基于加权Schatten-p范数最小化模型。利用Schatten-p范数作为秩函数的逼近函数对评分矩阵进行低秩约束;采用对奇异值加权的方式来避免对所有奇异值用同一值收缩的问题,以更好地逼近原始秩函数;采用近端交替线性化最小化方法来求解非凸最小化问题。MovieLens数据集上的实验结果表明,相比加权核范数模型(WNNM)、卷积矩阵分解模型(ConvMF)、融合多维语义表示的概率矩阵分解模型(MFMSR),该模型提高了预测的准确性,在推荐性能指标上明显优于对比模型。

The matrix completion model based on nuclear norm cannot provide high prediction accuracy in filling rating matrix because of imposing the same punishments to all singular values,and the nuclear norm may not approximate the rank function well in practice.To solve the above problems,a weighted Schatten-p norm minimization model was proposed.Schatten-p norm was used as the approximation function of the rank function,leading to a low rank constraint.The singular values were assigned different weights to avoid shrinking all singular values with the same value and better approximate the original rank function.The proximal alternating linearized minimization was used to solve the non-convex minimization problem of matrix completion.The experimental results on MovieLens dataset show that the proposed model improves the accuracy of prediction and is superior to the weighted nuclear norm minimization(WNNM)model,convolutional matrix factorization(ConvMF)model and probabilistic matrix factorization model based on multidimensional semantic representation learning(MFMSR).