论文标题
神经网络的基质分解
Matrix factorization with neural networks
论文作者
论文摘要
矩阵分解是在字典学习，推荐系统和机器学习的背景下遇到的重要数学问题。我们介绍了一种新的“拆卸”方案，将其映射到关联记忆的神经网络模型中，并对其性能进行详细的理论分析，表明拆卸能够分解较高的矩阵并有效地将其定位。我们基于对神经网络的地面搜索介绍了一种分解算法，该算法显示了与理论预测相匹配的性能。
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of associative memory and provide a detailed theoretical analysis of its performance, showing that decimation is able to factorize extensive-rank matrices and to denoise them efficiently. We introduce a decimation algorithm based on ground-state search of the neural network, which shows performances that match the theoretical prediction.
