A Biased Proportional-Integral-Derivative-Incorporated Latent Factor Analysis Model

Nowadays, as the number of items is increasing and the number of items that users have access to is limited, user-item preference matrices in recommendation systems are always sparse. This leads to a data sparsity problem. The latent factor analysis (LFA) model has been proposed as the solution to the data sparsity problem. As the basis of the LFA model, the singular value decomposition (SVD) model, especially the biased SVD model, has great recommendation effects in high-dimensional sparse (HiDs) matrices. However, it has the disadvantage of requiring several iterations before convergence. Besides, the model PID-incorporated SGD-based LFA (PSL) introduces the principle of discrete PID controller into the stochastic gradient descent (SGD), the learning algorithm of the SVD model. It could solve the problem of slow convergence speed, but its accuracy of recommendation needs to be improved. In order to make better solution, this paper fuses the PSL model with the biased SVD model, hoping to obtain better recommendation result by combining their advantages and reconciling their disadvantages. The experiments show that this biased PSL model performs better than the traditional matrix factorization algorithms on different sizes of datasets.