Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix factorization approximates the entries of the matrix by a simple, fixed function---namely, the inner product---acting on the latent feature vectors for the corresponding row and column. Here we consider replacing the inner product by an arbitrary function that we learn from the data at the same time as we learn the latent feature vectors. In particular, we replace the inner product by a multi-layer feed-forward neural network, and learn by alternating between optimizing the network for fixed latent features, and optimizing the latent features for a fixed network. The resulting approach---which we call neural network matrix factorization or NNMF, for short---dominates standard low-rank techniques on a suite of benchmark but is dominated by some recent proposals that also relax the low-rank assumption. Given the vast range of architectures, activation functions, regularizers, and optimization techniques that could be used within the NNMF framework, it seems likely the true potential of the approach has yet to be reached.

本文介绍一种基于神经网络与矩阵分解的方法，使用最优化技术得到潜在特征向量并据此构建神经网络，进而代替传统内积的矩阵分解方法，从而在一些测试数据集上达到更好的效果。

神经网络矩阵分解