Quality-of-Service (QoS) data plays a crucial role in cloud service selection. Since users cannot access all services, QoS can be represented by a high-dimensional and incomplete (HDI) matrix. Latent factor analysis (LFA) models have been proven effective as low-rank representation techniques for addressing this issue. However, most LFA models rely on first-order optimizers and use L2-norm regularization, which can lead to lower QoS prediction accuracy. To address this issue, this paper proposes a double regularized second-order latent factor (DRSLF) model with two key ideas: a) integrating L1-norm and L2-norm regularization terms to enhance the low-rank representation performance; b) incorporating second-order information by calculating the Hessian-vector product in each conjugate gradient step. Experimental results on two real-world response-time QoS datasets demonstrate that DRSLF has a higher low-rank representation capability than two baselines.

Abstract--A second-order-based latent factor (SLF) analysis model demonstrates superior performance in graph representation learning, particularly for high-dimensional and incomplete (HDI) interaction data, by incorporating the curvature information of the loss landscape. However, its objective function is commonly bi-linear and non-convex, causing the SLF model to suffer from a low convergence rate. To address this issue, this paper proposes a PID controller-incorporated SLF (PSLF) model, leveraging two key strategies: a) refining learning error estimation by incorporating the PID controller principles, and b) acquiring second-order information insights through Hessian-vector products. Experimental results on multiple HDI datasets indicate that the proposed PSLF model outperforms four state-of-the-art latent factor models based on advanced optimizers regarding convergence rates and generalization performance. In a recommender system, each user and item interaction can be labeled as a rating, describing the user's preference for an item.

Interactions among large number of entities is naturally high-dimensional and incomplete (HDI) in many big data related tasks. Behavioral characteristics of users are hidden in these interactions, hence, effective representation of the HDI data is a fundamental task for understanding user behaviors. Latent factor analysis (LFA) model has proven to be effective in representing HDI data. The performance of an LFA model relies heavily on its training process, which is a non-convex optimization. It has been proven that incorporating local curvature and preprocessing gradients during its training process can lead to superior performance compared to LFA models built with first-order family methods. However, with the escalation of data volume, the feasibility of second-order algorithms encounters challenges. To address this pivotal issue, this paper proposes a mini-block diagonal hessian-free (Mini-Hes) optimization for building an LFA model. It leverages the dominant diagonal blocks in the generalized Gauss-Newton matrix based on the analysis of the Hessian matrix of LFA model and serves as an intermediary strategy bridging the gap between first-order and second-order optimization methods. Experiment results indicate that, with Mini-Hes, the LFA model outperforms several state-of-the-art models in addressing missing data estimation task on multiple real HDI datasets from recommender system. (The source code of Mini-Hes is available at https://github.com/Goallow/Mini-Hes)

High-dimensional and incomplete (HDI) matrix contains many complex interactions between numerous nodes. 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 only considers the current learning error to compute the stochastic gradient without considering the historical and future state of the learning error. To address this critical issue, this paper innovatively proposes an ADRC-incorporated SGD (ADS) algorithm by refining the instance learning error by considering the historical and future state by following the principle of an ADRC controller. With it, an ADS-based LFA model is further achieved for fast and accurate latent factor analysis on an HDI matrix. Empirical studies on two HDI datasets demonstrate that the proposed model outperforms the state-of-the-art LFA models in terms of computational efficiency and accuracy for predicting the missing data of an HDI matrix.

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.

High-Dimensional and Incomplete matrices, which usually contain a large amount of valuable latent information, can be well represented by a Latent Factor Analysis model. The performance of an LFA model heavily rely on its optimization process. Thereby, some prior studies employ the Particle Swarm Optimization to enhance an LFA model's optimization process. However, the particles within the swarm follow the static evolution paths and only share the global best information, which limits the particles' searching area to cause sub-optimum issue. To address this issue, this paper proposes a Dynamic-neighbor-cooperated Hierarchical PSO-enhanced LFA model with two-fold main ideas. First is the neighbor-cooperated strategy, which enhances the randomly chosen neighbor's velocity for particles' evolution. Second is the dynamic hyper-parameter tunning. Extensive experiments on two benchmark datasets are conducted to evaluate the proposed DHPL model. The results substantiate that DHPL achieves a higher accuracy without hyper-parameters tunning than the existing PSO-incorporated LFA models in representing an HDI matrix.

Extracting the latent information in high-dimensional and incomplete matrices is an important and challenging issue. The Latent Factor Analysis (LFA) model can well handle the high-dimensional matrices analysis. Recently, Particle Swarm Optimization (PSO)-incorporated LFA models have been proposed to tune the hyper-parameters adaptively with high efficiency. However, the incorporation of PSO causes the premature problem. To address this issue, we propose a sequential Adam-adjusting-antennae BAS (A2BAS) optimization algorithm, which refines the latent factors obtained by the PSO-incorporated LFA model. The A2BAS algorithm consists of two sub-algorithms. First, we design an improved BAS algorithm which adjusts beetles' antennae and step-size with Adam; Second, we implement the improved BAS algorithm to optimize all the row and column latent factors sequentially. With experimental results on two real high-dimensional matrices, we demonstrate that our algorithm can effectively solve the premature convergence issue.

Abstract--High-dimensional and incomplete (HDI) data holds tremendous interactive information in various industrial applications. A latent factor (LF) model is remarkably effective in extracting valuable information from HDI data with stochastic gradient decent (SGD) algorithm. However, an SGD-based LFA model suffers from slow convergence since it only considers the current learning error. To address this critical issue, this paper proposes a Nonlinear PID-enhanced Adaptive Latent Factor (NPALF) model with two-fold ideas: 1) rebuilding the learning error via considering the past learning errors following the principle of a nonlinear PID controller; b) implementing all parameters adaptation effectively following the principle of a particle swarm optimization (PSO) algorithm. Experience results on four representative HDI datasets indicate that compared with five state-of-the-art LFA models, the NPALF model achieves better convergence rate and prediction accuracy for missing data of an HDI data.

Stochastic gradient descent (SGD) algorithm is an effective learning strategy to build a latent factor analysis (LFA) model on a high-dimensional and incomplete (HDI) matrix. A particle swarm optimization (PSO) algorithm is commonly adopted to make an SGD-based LFA model's hyper-parameters, i.e, learning rate and regularization coefficient, self-adaptation. However, a standard PSO algorithm may suffer from accuracy loss caused by premature convergence. To address this issue, this paper incorporates more historical information into each particle's evolutionary process for avoiding premature convergence following the principle of a generalized-momentum (GM) method, thereby innovatively achieving a novel GM-incorporated PSO (GM-PSO). With it, a GM-PSO-based LFA (GMPL) model is further achieved to implement efficient self-adaptation of hyper-parameters. The experimental results on three HDI matrices demonstrate that the GMPL model achieves a higher prediction accuracy for missing data estimation in industrial applications.

A High-dimensional and sparse (HiDS) matrix is frequently encountered in a big data-related application like an e-commerce system or a social network services system. To perform highly accurate representation learning on it is of great significance owing to the great desire of extracting latent knowledge and patterns from it. Latent factor analysis (LFA), which represents an HiDS matrix by learning the low-rank embeddings based on its observed entries only, is one of the most effective and efficient approaches to this issue. However, most existing LFA-based models perform such embeddings on a HiDS matrix directly without exploiting its hidden graph structures, thereby resulting in accuracy loss. To address this issue, this paper proposes a graph-incorporated latent factor analysis (GLFA) model. It adopts two-fold ideas: 1) a graph is constructed for identifying the hidden high-order interaction (HOI) among nodes described by an HiDS matrix, and 2) a recurrent LFA structure is carefully designed with the incorporation of HOI, thereby improving the representa-tion learning ability of a resultant model. Experimental results on three real-world datasets demonstrate that GLFA outperforms six state-of-the-art models in predicting the missing data of an HiDS matrix, which evidently supports its strong representation learning ability to HiDS data.