  A high-dimensional and incomplete (HDI) matrix can describe the complex
interactions among numerous nodes in various big data-related applications. A
stochastic gradient descent (SGD)-based latent factor analysis (LFA) model is
remarkably effective in extracting valuable information from an HDI matrix.
However, such a model commonly encounters the problem of slow convergence
because a standard SGD algorithm learns a latent factor relying on the
stochastic gradient of current instance error only without considering past
update information. To address this critical issue, this paper innovatively
proposes a Fuzzy PID-incorporated SGD (FPS) algorithm with two-fold ideas: 1)
rebuilding the instance learning error by considering the past update
information in an efficient way following the principle of PID, and 2)
implementing hyper-parameters and gain parameters adaptation following the
fuzzy rules. With it, an FPS-incorporated LFA model is further achieved for
fast processing an HDI matrix. Empirical studies on six HDI datasets
demonstrate that the proposed FPS-incorporated LFA model significantly
outperforms the state-of-the-art LFA models in terms of computational
efficiency for predicting the missing data of an HDI matrix with competitive
accuracy.
