拟合矩阵与两阶融合迭代加速推荐算法

传统的矩阵分解模型无法充分探索用户与物品在均值、偏置和特征之间的内在联系，提出拟合矩阵模型，通过构建用户与物品矩阵分别代表用户与物品特性来提高预测性能。矩阵分解模型在推荐系统领域有精度优势，但求解模型参数最常用的梯度下降法收敛速度缓慢，因此考虑与拟牛顿法融合，加快收敛速度。提出的算法命名为拟合矩阵与两阶融合迭代加速推荐算法（fitting matrix and two orders fusion iterative，FAST），实验表明，FAST算法比传统的非负矩阵分解（NMF）、奇异值矩阵分解（SVD）、正则化奇异值矩阵分解（RSVD）在平均绝对误差（MAE）与均方根误差（RMSE）上有下降，在迭代效率上有显著提高，缓解了精度与迭代效率难以平衡的问题。

Accelerating recommendation algorithm using fitting matrix and two orders fusion iterative

The traditional matrix decomposition model can not fully explored the intrinsic relationship between the user and the object in the mean, bias and characteristics. This paper proposed a fitting matrix model to improve the prediction performance by constructing the user and the item matrix to represent the characteristics of the user and the item respectively. The matrix decomposition model had the advantage of accuracy in the field of recommender system, but the gradient descent method, which was the most popular method to train parameters of model, had a slow convergence speed. To resolve the above defects, this paper considered to accelerate the convergence speed using the convergence of quasi Newton method, and named the proposed algorithm as fitting matrix and two orders fusion iterative(FAST) algorithm. The experimental results show that the FAST algorithm is better than the traditional non negative matrix decomposition(NMF), singular value matrix decomposition(SVD), and the regularized singular value matrix decomposition(RSVD). FAST algorithm has a decrease with regard to the mean absolute error(MAE) and the root mean square error(RMSE), and has a significant improvement in the iterative efficiency, which alleviates the problem that the accuracy is difficult to balance with the efficiency of the iteration.