  A high-dimensional and incomplete (HDI) matrix frequently appears in various
big-data-related applications, which demonstrates the inherently non-negative
interactions among numerous nodes. A non-negative latent factor (NLF) model
performs efficient representation learning to an HDI matrix, whose learning
process mostly relies on a single latent factor-dependent, non-negative and
multiplicative update (SLF-NMU) algorithm. However, an SLF-NMU algorithm
updates a latent factor based on the current update increment only without
appropriate considerations of past learning information, resulting in slow
convergence. Inspired by the prominent success of a proportional-integral (PI)
controller in various applications, this paper proposes a
Proportional-Integral-incorporated Non-negative Latent Factor (PI-NLF) model
with two-fold ideas: a) establishing an Increment Refinement (IR) mechanism via
considering the past update increments following the principle of a PI
controller; and b) designing an IR-based SLF-NMU (ISN) algorithm to accelerate
the convergence rate of a resultant model. Empirical studies on four HDI
datasets demonstrate that a PI-NLF model outperforms the state-of-the-art
models in both computational efficiency and estimation accuracy for missing
data of an HDI matrix. Hence, this study unveils the feasibility of boosting
the performance of a non-negative learning algorithm through an error feedback
controller.
