This paper studies the key problems of bearing fault diagnosis of high-speed train. As the core component of the train operation system, the health of bearings is directly related to the safety of train operation. The traditional diagnostic methods are facing the challenge of insufficient diagnostic accuracy under complex conditions. To solve these problems, we propose a novel Neural Factorization-based Classification (NFC) framework for bearing fault diagnosis. It is built on two core idea: 1) Embedding vibration time series into multiple mode-wise latent feature vectors to capture diverse fault-related patterns; 2) Leveraging neural factorization principles to fuse these vectors into a unified vibration representation. This design enables effective mining of complex latent fault characteristics from raw time-series data. We further instantiate the framework with two models CP-NFC and Tucker-NFC based on CP and Tucker fusion schemes, respectively. Experimental results show that both models achieve superior diagnostic performance compared with traditional machine learning methods. The comparative analysis provides valuable empirical evidence and practical guidance for selecting effective diagnostic strategies in high-speed train bearing monitoring.

Water quality monitoring is a core component of ecological environmental protection. However, due to sensor failure or other inevitable factors, data missing often exists in long-term monitoring, posing great challenges in water quality analysis. This paper proposes a Neural Tucker Convolutional Network (NTCN) model for water quality data imputation, which features the following key components: a) Encode different mode entities into respective embedding vectors, and construct a Tucker interaction tensor by outer product operations to capture the complex mode-wise feature interactions; b) Use 3D convolution to extract fine-grained spatiotemporal features from the interaction tensor. Experiments on three real-world water quality datasets show that the proposed NTCN model outperforms several state-of-the-art imputation models in terms of accuracy. In advancing the modernization drive for harmonious coexistence between humans and nature, water quality monitoring plays an irreplaceable role [1]-[7].

Air turbulence refers to the disordered and irregular motion state generated by drastic changes in velocity, pressure, or direction during airflow. Various complex factors lead to intricate low-altitude turbulence outcomes. Under current observational conditions, especially when using only wind profile radar data, traditional methods struggle to accurately predict turbulence states. Therefore, this paper introduces a NeuTucker decomposition model utilizing discretized data. Designed for continuous yet sparse three-dimensional wind field data, it constructs a low-rank Tucker decomposition model based on a Tucker neural network to capture the latent interactions within the three-dimensional wind field data. Therefore, two core ideas are proposed here: 1) Discretizing continuous input data to adapt to models like NeuTucF that require discrete data inputs. 2) Constructing a four-dimensional Tucker interaction tensor to represent all possible spatio-temporal interactions among different elevations and three-dimensional wind speeds. In estimating missing observations in real datasets, this discretized NeuTucF model demonstrates superior performance compared to various common regression models.

The integrity of Water Quality Data (WQD) is critical in environmental monitoring for scientific decision-making and ecological protection. However, water quality monitoring systems are often challenged by large amounts of missing data due to unavoidable problems such as sensor failures and communication delays, which further lead to water quality data becoming High-Dimensional and Sparse (HDS). Traditional data imputation methods are difficult to depict the potential dynamics and fail to capture the deep data features, resulting in unsatisfactory imputation performance. To effectively address the above issues, this paper proposes a Nonlinear Low-rank Representation model (NLR) with Convolutional Neural Networks (CNN) for imputing missing WQD, which utilizes CNNs to implement two ideas: a) fusing temporal features to model the temporal dependence of data between time slots, and b) Extracting nonlinear interactions and local patterns to mine higher-order relationships features and achieve deep fusion of multidimensional information. Experimental studies on three real water quality datasets demonstrate that the proposed model significantly outperforms existing state-of-the-art data imputation models in terms of estimation accuracy. It provides an effective approach for handling water quality monitoring data in complex dynamic environments.

Modern intelligent transportation systems rely on accurate spatiotemporal traffic analysis to optimize urban mobility and infrastructure resilience. However, pervasive missing data caused by sensor failures and heterogeneous sensing gaps fundamentally hinders reliable traffic modeling. This paper proposes a Neural Canonical Polyadic Factorization (NCPF) model that synergizes low-rank tensor algebra with deep representation learning for robust traffic data imputation. The model innovatively embeds CP decomposition into neural architecture through learnable embedding projections, where sparse traffic tensors are encoded into dense latent factors across road segments, time intervals, and mobility metrics. A hierarchical feature fusion mechanism employs Hadamard products to explicitly model multilinear interactions, while stacked multilayer perceptron layers nonlinearly refine these representations to capture complex spatiotemporal couplings. Extensive evaluations on six urban traffic datasets demonstrate NCPF's superiority over six state-of-the-art baselines. By unifying CP decomposition's interpretable factor analysis with neural network's nonlinear expressive power, NCPF provides a principled yet flexible approaches for high-dimensional traffic data imputation, offering critical support for next-generation transportation digital twins and adaptive traffic control systems.

High-dimensional and incomplete (HDI) data, characterized by massive node interactions, have become ubiquitous across various real-world applications. Second-order latent factor models have shown promising performance in modeling this type of data. Nevertheless, due to the bilinear and non-convex nature of the SLF model's objective function, incorporating a damping term into the Hessian approximation and carefully tuning associated parameters become essential. To overcome these challenges, we propose a new approach in this study, named the adaptive cubic regularized second-order latent factor analysis (ACRSLF) model. The proposed ACRSLF adopts the two-fold ideas: 1) self-tuning cubic regularization that dynamically mitigates non-convex optimization instabilities; 2) multi-Hessian-vector product evaluation during conjugate gradient iterations for precise second-order information assimilation. Comprehensive experiments on two industrial HDI datasets demonstrate that the ACRSLF converges faster and achieves higher representation accuracy than the advancing optimizer-based LFA models.

Intelligent transportation systems (ITS) rely heavily on comp lete and high - quality spatiotemporal traffic data to achieve optimal performance. Nevertheless, in real - word traffic data collection processes, issues such as communication failures and sensor malfunctions often lead to incomplete or corrupted datasets, th ereby posing significant challenges to the advancement of ITS. Among various methods for imputing missing spatiotemporal traffic data, the latent factorization of tensors (LFT) model has emerged as a widely adopted and effective solution. However, conventi onal LFT models typically employ the standard L 2 - norm in their learning objective, which makes them vulnerable to the influence of outliers. To overcome this limitation, this paper proposes a threshold distance weighted (TDW) loss - incorporated Latent Facto ri zation of Tensors ( TDW LFT) model . The proposed loss function effectively reduces the model's sensitivity to outliers by assigning differentiated weights to individual samples. Extensive experiments conducted on two traffic speed datasets sourced from div erse urban environments confirm that the proposed TDW LFT model consistently outperforms state - of - the - art approaches in terms of both in both prediction accuracy and computational efficiency .

Low - rank representat i on learn ing ha s emerged as a powerful tool for recoverin g missing values i n power load data due to its ability to exploit the inherent low - dimensional structures of spatiotemporal measurements. Among various techniques, low - rank factorization models are f a vou red f o r t he ir efficiency and interpretability . Howeve r, their performan ce is highly sensitive to the choice of regularization parameter s, which are typically fixed or manually tuned, resulting in limited generalization capability or slow convergenc e in pra ctica l sc en arios. In this paper, we propo se a Regular ization - optimized Low - Rank Factorization, which introduces a Proportional - Integral - Derivative controller to adaptively adju st the regularization coefficient . Furthe rmore, we provide a detailed algori t hmi c com plex i t y analysis, showing that our method preser ves the computatio nal efficiency of stochastic gradient descent while improving ad aptivity. Experimental results on real - world power load datasets validate the superiority of our method in both imput a tio n acc urac y and training efficiency compared to existi ng baselines.

With the development of smart grids, High-Dimensional and Incomplete (HDI) Power Load Monitoring (PLM) data challenges the performance of Power Load Forecasting (PLF) models. In this paper, we propose a potential characterization model VAE-LF based on Variational Autoencoder (VAE) for efficiently representing and complementing PLM missing data. VAE-LF learns a low-dimensional latent representation of the data using an Encoder-Decoder structure by splitting the HDI PLM data into vectors and feeding them sequentially into the VAE-LF model, and generates the complementary data. Experiments on the UK-DALE dataset show that VAE-LF outperforms other benchmark models in both 5% and 10% sparsity test cases, with significantly lower RMSE and MAE, and especially outperforms on low sparsity ratio data. The method provides an efficient data-completion solution for electric load management in smart grids.

Link prediction in dynamic networks remains a fundamental challenge in network science, requiring the inference of potential interactions and their evolving strengths through spatiotemporal pattern analysis. Traditional static network methods have inherent limitations in capturing temporal dependencies and weight dynamics, while tensor - based methods offer a promising paradigm by encoding dynamic networks into high - order tensors to explicitly model multidimensional interactions across nodes and time. Among them, tensor wheel decomposition (TWD) stands out for its innovative topological structure, which decomposes high - order tensors into cyclic factors and core tensors to maintain structural integrity. To improve the prediction accuracy, this study introduces a PID - controll ed tensor wheel decomposition (PTWD) model, which mainly adopts the following two ideas: 1) exploiting the representation power of TWD to capture the latent features of d ynamic network topology and weight evolution, and 2) integrating the proportional - integral - derivative (PID) control principle into the optimization process to obtain a stable model parameter learning scheme. The performance on four real datasets verifies that the proposed PTWD model has more accurate link prediction capabilities compared to other models.