Since similar users frequently exhibit similar Quality of Service (QoS) when accessing similar services, effectively capturing neighborhood information hidden in QoS data becomes critical for latent factorization of tensor (LFT)-based QoS estimators. Current LFT models either calculate the complete set of neighborhoods or do not consider neighborhoods, resulting in a rapid rise in model complexity and poor estimation accuracy. Moreover, not every neighbor in the neighborhood set is beneficial to the user/service entity. To address these limitations, this study proposes a sampling-neighborhood-regularized latent factorization of tensor (SNLFT) model with three key ideas: 1) extracting primal latent factors (LFs), which are obtained to express related entities on the basis of high-dimensional and incomplete QoS data; 2) constructing the sampling-neighborhood set, which is acquired using the Gibbs sampling to reflect the similarities between the primal LF vectors of entities over time; 3) developing a sampling-neighborhood-regularized LFT model, where all the sampling neighborhoods of entities and L2-norm of desirable LFs are employed to regularize the objective function. Extensive experiments on eight dynamic QoS datasets demonstrate that SNLFT significantly outperforms state-of-the-art models in both estimation accuracy and computational efficiency.

The traditional nonnegative latent factorization of tensors (NLFTs) models can effectively represent high-dimensional and incomplete (HDI) tensors, but they currently face two main problems: 1) existing models are linear and cannot capture the nonlinear features of HDI tensors and 2) they rely on random initialization of nonnegative parameter and constraint-combined training schemes. To address these issues, this article proposes a neural NLFTs model with acceleration and unconstraint. The main ideas are given as follows: 1) utilizing a neural network (NN) structure and a nonlinear activation function to capture the nonlinear features within the HDI tensor accurately; 2) constructing a nonnegative mapping domain that transfers nonnegativity constraints from latent factors (LFs) to output decision parameters via a single-element-dependent mapping function, enabling an unconstrained optimization framework; and 3) utilizing the highly compatible momentum-incorporated stochastic gradient descent (SGD) algorithm as the backward propagation (BP) learning scheme of the model, which not only ensures training effectiveness and scalability but also accelerates convergence. Empirical studies on ten HDI tensors demonstrate that the proposed model achieves impressive estimation accuracy and per-iteration time cost compared to state-of-the-art models.

Traffic data prediction is a crucial component of Intelligent Transport Systems (ITS) as it contributes significantly to real-time navigation and congestion management. However, due to incomplete deployment of sensor and instability of data transmission, the traffic data that we collect is usually a high-dimensional and incomplete (HDI) matrix or tensor. Currently, there are two challenges with traffic data prediction as follows: a) Most of the existing models are designed for a full set of data, but traffic data are unavoidably missing. b) Most of the existing models often suffer from excessive complexity due to long sequences. To address these issues, we propose a novel3D Convolution-IncorporatedDimensionPreserved Decomposition (3DCIDP) model for traffic data prediction with three main fold ideas: a) enhancing the low-rank property of traffic data to accurately capture its structure, b) learning the constraints of historical sequences to predict sequences through representation modelling and c) capturing spatio-temporal interaction information in traffic data through multidimensional interaction features. To evaluate the performance of the proposed 3DCIDP, we conduct extensive experiments using five publicly available datasets with three different missing rates. When the proposed 3DCIDP is compared to state-of-the-art models, experimental results show that the Root Mean Square Error (RMSE) is reduced by an average of 4.22% and the training time is reduced by an average of 89.76% on the large-scale traffic datasets.

High-dimensional and incomplete (HDI) data are involved frequently in big data-related industrial applications. Latent factor (LF) analysis aims at extracting the knowledge of great value from such extremely sparse HDI data efficiently. Non-negative LF models based on the single LF-dependent, non-negative, and multiplicative update rules exactly are the representative of LF analysis. However, these models face low generalization dilemma due to incompatible with general unconstrained optimization techniques. To address this issue, this article proposes a novel momentum-accelerated and biased unconstrained non-negative latent factor (MBUNLF) model, which matches with unconstrained optimization techniques. The proposed MBUNLF model is built on three main ideas: (a) Improving the generalization through a non-negative mapping function; (b) Capturing information among different entities through linear biases; (c) Accelerating convergence during the training process through generalized momentum method. Empirical studies on six datasets from industrial applications indicate that the proposed MBUNLF model outperforms nine state-of-the-art models when processing HDI data, reducing the root mean square error by 19.47% on average. It demonstrates the validity of the MBUNLF model in extracting non-negative LFs from HDI data.

High-Dimensional and Incomplete (HDI) tensors contain a wealth of knowledge and patterns, which are typically utilized to characterize complex relationships between entities in a variety of industrial applications. Currently, the neural network-based tensor factorization model has shown superiority when handling the missing data in HDI tensors. However, it only uses the outer product of latent factors (LFs) of entities and neglects the interactions between the LF. In addition, the simple linear operation does not consider the nonlinear structure of the HDI tensor. To overcome the aforementioned issues, an Attention-mechanism-based Neural Latent-Factorization-of-Tensors (ANLFT) model is provided in this article. It encompasses three primary ideas: (a) incorporating the theory of neural networks with the latent factorization of tensor to construct the nonlinear structure in the HDI tensor effectively; (b) adopting the attention mechanism to depict the interactions between LF; (c) using the position-transitional particle swarm optimization backward propagation learning ( \(\rm{P}^{2}\) BP) scheme to train the ANLFT model efficiently. The experimental results on eight HDI datasets show that the ANLFT model can obtain higher estimation performance gain than state-of-the-art models. The convergence performance of the proposed model is also competitive with that of state-of-the-art models.

Predicting student performance (PSP) is critical to intelligent tutoring systems in online education services. Accurate predictions enable data-driven decision making and facilitate the implementation of timely educational interventions. While previous approaches, such as cognitive diagnosis models and data mining techniques, have demonstrated effectiveness with small-scale and static datasets, they face significant challenges in large-scale online learning environments. In these settings, vast volumes of learning responses are continuously generated as students engage with exercises. Those responses are characterized by high dimensionality and incompleteness (HDI) and often manifest as streaming data, which limits the applicability of most existing prediction methods, therefore posing a new challenge to traditional PSP tasks. To remedy the void of PSP in the HDI and incremental scenario, we propose an incremental nonlinear co-latent factor analysis (IN-CoLFA) model, which enhances latent factor analysis – an element-wise learning framework – by incorporating a co-factorization technique and integrating a neural network-inspired structure. To facilitate incremental learning, we develop momentum-accelerated stochastic gradient-based algorithms, which enable the model to perform offline training on historical data and continuously refine its predictions as new student performance becomes available. Experiments on several real-world datasets demonstrate the efficacy and efficiency of our approach in both stationary and incremental PSP tasks under HDI conditions.

Time-varying quality-of-service (QoS) data are usually utilized for Web service evaluation and selection. To accurately estimate the unknown information in time-varying QoS data, it is crucial to capture the temporal patterns hidden in the known data. The Non-negative Latent Factorization of Tensors (NLFT) model has performed well in describing the temporal patterns in time-varying QoS data. However, it assigns a single bias to each dimension of the target QoS tensor, making it suffer from estimation accuracy loss when describing the fluctuations of time-varying QoS data. To address this vital issue, this paper proposes an Adaptively Bias-extended NLFT (ABNT) model based on the fuzzy logic with two-fold ideas: a) extending the linear biases on each dimension of tensor for describing the complex fluctuations of QoS data precisely, b) building a fuzzy logic-incorporated particle swarm optimization algorithm to establish a self-adaptation mechanism for the count of extended linear biases and regularization coefficients. Detailed algorithms and analyses are provided for the proposed ABNT model. Empirical studies on two practical time-varying QoS datasets indicate that the estimation accuracy of the ABNT model outperforms that of state-of-the-art QoS data estimation models (with an average 23.94% improvement in MAE).

high-dimensional and incomplete (HDI) matrices are commonly encountered in a variety of big data-related industrial applications, which describe complex interactions between entities. The complete interaction relationship in the HDI matrix is essential to deal with various problems such as pattern recognition in industrial applications. Therefore, estimating the missing data in the HDI matrix is crucial. latent factor analysis (LFA) models have achieved advanced results in solving such problems. However, the existing LFA models cannot model the nonlinear structure hidden in the HDI matrix. neural networks (NNs) can handle the nonlinearity in the HDI data, but their high estimation accuracy relies on high computation cost and storage burden. To address the aforementioned problems, this article proposes a novel NNLFA model. It contains the following primary ideas: 1) it can model the nonlinear structure of the HDI matrix efficiently through NNs and 2) it incorporates the NNs into the LFA model to improve estimation accuracy while maintaining high computational and storage efficiency. To validate the superiority of the NNLFA model, experiments with six state-of-the-art models are conducted on six practical industrial application datasets. The experimental results indicate that the NNLFA model enhances estimation accuracy by up to 33.3%. In addition, NNLFA model shows strong competitiveness in terms of both time and storage efficiency when compared to baseline models.

Time-varying quality-of-service (QoS) data is often used to measure the performance of Web services. It is vital to capture the temporal pattern hidden in such time-varying QoS data for estimating unknown ones. A Nonnegative Latent Factorization of Tensors (NLFT) model is highly effective and efficient in describing temporal patterns. However, an NLFT model assigns a single bias into each order of the target QoS data tensor, making it unable to accurately describe the fluctuations of time-varying QoS data, thus impairing its estimation performance. To address this issue, this paper proposes an Extended linear Biases Nonnegative Latent factorization of tensor (EBNL) model with two-fold ideas: a) incorporating multiple linear biases into the model for describing QoS fluctuations precisely, and b) adopting a particle swarm optimization (PSO) algorithm to make the scale of linear biases self-adaptive. Experiments on two time-varying QoS data generated by real applications indicate that compared with several state-of-the-art QoS estimators, the proposed EBNL model achieves higher estimation accuracy for unknown QoS data.

Intelligent Transportation Systems (ITSs) are vital for alleviating traffic congestion and improving traffic efficiency. Due to the delay of network transmission and failure of detectors, massive missing traffic data are often produced in ITSs, which evidently decreases the accuracy of decision-making in road traffic management. Hence, how establishing a precise and efficient estimation of missing traffic data becomes a hot yet thorny issue. Low-rank matrix completion (LR-MC) model has proven to be highly effective to address this issue owing to its fine representativeness of such high-dimensional and incomplete data. However, the existing LR-MC models mostly fail to model the inherently temporal and spatial correlations hidden in traffic network structure, resulting in low estimation accuracy. To improve it, this paper proposes a Hessian regularization spatio-temporal low rank (HRST-LR) algorithm with three main-fold ideas: a) imposing low-rank property into the global features of a traffic matrix for precisely learning its structure, b) capturing the temporal evolvement via a second-order difference of time-series constraint, and c) modeling the similar space of road segments through a Hessian regularization spatial constraint, thus exploring the local correlation between road segments for representing the spatial patterns in the traffic data. Experimental results on four traffic data sets prove that HRST-LR outperforms several state-of-the-art methods in the missing traffic data estimation with the root mean squared error improvements often higher than 14% when the missing rate is 90%. Hence, the HRST-LR algorithm is highly valuable for traffic data imputation with the need of performing spatio-temporal low-rank analysis.