Learning matrix factorization with scalable distance metric and regularizer.

Matrix factorization has always been an encouraging field, which attempts to extract discriminative features from high-dimensional data. However, it suffers from negative generalization ability and high computational complexity when handling large-scale data. In this paper, we propose a learnable deep matrix factorization via the projected gradient descent method, which learns multi-layer low-rank factors from scalable metric distances and flexible regularizers. Accordingly, solving a constrained matrix factorization problem is equivalently transformed into training a neural network with an appropriate activation function induced from the projection onto a feasible set. Distinct from other neural networks, the proposed method activates the connected weights not just the hidden layers. As a result, it is proved that the proposed method can learn several existing well-known matrix factorizations, including singular value decomposition, convex, nonnegative and semi-nonnegative matrix factorizations. Finally, comprehensive experiments demonstrate the superiority of the proposed method against other state-of-the-arts.