Small Sample Data Research Articles

Active Fault Tolerant Nonsingular Terminal Sliding Mode Control for Electromechanical System Based on Support Vector Machine

Effective fault diagnosis and fault-tolerant control method for aeronautics electromechanical actuator is concerned in this paper. By borrowing the advantages of model-driven and data-driven methods, a fault tolerant nonsingular terminal sliding mode control method based on support vector machine (SVM) is proposed. A SVM is designed to estimate the fault by off-line learning from small sample data with solving convex quadratic programming method and is introduced into a high-gain observer, so as to improve the state estimation and fault detection accuracy when the fault occurs. The state estimation value of the observer is used for state reconfiguration. A novel nonsingular terminal sliding mode surface is designed, and Lyapunov theorem is used to derive a parameter adaptation law and a control law. It is guaranteed that the proposed controller can achieve asymptotical stability which is superior to many advanced fault-tolerant controllers. In addition, the parameter estimation also can help to diagnose the system faults because the faults can be reflected by the parameters variation. Extensive comparative simulation and experimental results illustrate the effectiveness and advancement of the proposed controller compared with several other main-stream controllers.

Relative permeability estimation using mercury injection capillary pressure measurements based on deep learning approaches

Relative permeability (RP) curves which provide fundamental insights into porous media flow behavior serve as critical parameters in reservoir engineering and numerical simulation studies. However, obtaining accurate RP curves remains a challenge due to expensive experimental costs, core contamination, measurement errors, and other factors. To address this issue, an innovative approach using deep learning strategy is proposed for the prediction of rock sample RP curves directly from mercury injection capillary pressure (MICP) measurements which include the mercury injection curve, mercury withdrawal curve, and pore size distribution. To capture the distinct characteristics of different rock samples' MICP curves effectively, the Gramian Angular Field (GAF) based graph transformation method is introduced for mapping the curves into richly informative image forms. Subsequently, these 2D images are combined into three-channel red, green, blue (RGB) images and fed into a Convolutional Long Short-Term Memory (ConvLSTM) model within our established self-supervised learning framework. Simultaneously the dependencies and evolutionary sequences among image samples are captured through the limited MICP-RP samples and self-supervised learning framework. After that, a highly generalized RP curve calculation proxy framework based on deep learning called RPCDL is constructed by the autonomously generated nearly infinite training samples. The remarkable performance of the proposed method is verified with the experimental data from rock samples in the X oilfield. When applied to 37 small-sample data spaces for the prediction of 10 test samples, the average relative error is 3.6%, which demonstrates the effectiveness of our approach in mapping MICP experimental results to corresponding RP curves. Moreover, the comparison study against traditional CNN and LSTM illustrated the great performance of the RPCDL method in the prediction of both So and Sw lines in oil–water RP curves. To this end, this method offers an intelligent and robust means for efficiently estimating RP curves in various reservoir engineering scenarios without costly experiments.

Abnormal Traffic Detection System Based on Feature Fusion and Sparse Transformer

This paper presents a feature fusion and sparse transformer-based anomalous traffic detection system (FSTDS). FSTDS utilizes a feature fusion network to encode the traffic data sequences and extracting features, fusing them into coding vectors through shallow and deep convolutional networks, followed by deep coding using a sparse transformer to capture the complex relationships between network flows; finally, a multilayer perceptron is used to classify the traffic and achieve anomaly traffic detection. The feature fusion network of FSTDS improves feature extraction from small sample data, the deep encoder enhances the understanding of complex traffic patterns, and the sparse transformer reduces the computational and storage overhead and improves the scalability of the model. Experiments demonstrate that the number of FSTDS parameters is reduced by up to nearly half compared to the baseline, and the success rate of anomalous flow detection is close to 100%.

Deep-Learning Correction Methods for Weather Research and Forecasting (WRF) Model Precipitation Forecasting: A Case Study over Zhengzhou, China

Systematic biases and coarse resolutions are major limitations of current precipitation datasets. Many studies have been conducted for precipitation bias correction and downscaling. However, it is still challenging for the current approaches to handle the complex features of hourly precipitation, resulting in the incapability of reproducing small-scale features, such as extreme events. In this study, we proposed a deep-learning model called PBT (Population-Based Training)-GRU (Gate Recurrent Unit) based on numerical model NWP gridded forecast data and observation data and employed machine-learning (ML) methods, such as Random Forest (RF), Support Vector Machine (SVM), K-Nearest Neighbor (KNN), and Gradient-Boosted Decision Tree (GBDT), to correct the WRF hourly precipitation forecasts. To select the evaluation method, we conducted a sample balance experiment and found that when the proportion of positive and negative samples was 1:1, the Threat Score (TS) and accuracy scores were the highest, while the Probability of Detection (POD) score was slightly lower. The results showed that: (1) the overall errors of the PBT-GRU model were relatively smaller, and its root mean square error (RMSE) was only 1.12 mm, which was reduced by 63.04%, 51.72%, 58.36%, 37.43%, and 26.32% compared to the RMSE of WRF, SVM, KNN, GBDT, and RF, respectively; and (2) according to the Taylor diagram, the standard deviation (σn) and correlation coefficient (r) of PBT-GRU were 1.02 and 0.99, respectively, while the σn and r of RF were 1.12 and 0.98, respectively. Furthermore, the σn and r of the SVM, GBDT, and KNN models were between those of the above models, with values of 1.24 and 0.95, 1.15 and 0.97, and 1.26 and 0.93, respectively. Based on a comprehensive analysis of the TS, accuracy, RMSE, r and σn, the PBT-GRU model performed the best, with a significantly better correction effect than that of the ML methods, resulting in an overall performance ranking of PBT-GRU > RF > GBDT > SVM > KNN. This study provides a hint of the possibility that the proposed PBT-GRU model can outperform model precipitation correction based on a small sample of one-station data. Thus, due to its promising performance and excellent robustness, we recommend adopting the proposed PBT-GRU model for precipitation correction in business applications.

An artificial neural network method for probabilistic life prediction of corroded reinforced concrete

Corroded reinforced concrete is affected by many factors. Therefore, the effects of these uncertainties should be considered when predicting fatigue life. However, artificial neural networks cannot determine the uncertainty of fatigue life. This paper establishes a new artificial neural network method to solve this problem. First, survival rates are obtained using the minimum number of specimens method. Second, the samples are divided. Then, a decision tree is used to determine the uncertainty of the test sample using corrosion and loading conditions. Finally, an artificial neural network is used to predict the fatigue life of the test sample using the survival rate, corrosion conditions, and loading conditions. If the training samples entered the artificial neural network are small sample data, the sample data are expanded using a beta-variational autoencoder with sample division. The established method is evaluated using fatigue test data from corroded reinforced concrete. Moreover, the evaluation results show that the established method can effectively predict the survival rate and fatigue life.

An element perception and state recognition method oriented to complex assembled product

Quality inspection during assembly process has an important impact on the performance and service life of the final product. Automated inspection solutions based on machine vision and artificial intelligence greatly improve the efficiency of inspection. However, the current mainstream large-scene inspection solutions, such as mobile vision platforms, are difficult to apply widely due to cost issues. Therefore, portable vision inspection solutions have gradually gained attention. However, the bottleneck technologies that limit this solution are full-element perception and occlusion judgment under free viewing angle, robust object matching method. To address the above problems, This paper proposes a free-viewpoint-based element perception and state recognition scheme. An improved structure estimation model is adopted to establish a bridge between virtual and actual mapping under the support of small-sample data, and all elements are located and occlusion analyzed by a 3D model-constrained view evolution algorithm. In addition, a hierarchy matching and optimization method is established to complete visual analysis. Experimental results show that this scheme performs well in structure estimation, element localization, occlusion judgment, state recognition, and work efficiency, demonstrating high application value.

Active learning driven discovery of novel alloyed catalysts for selective ammonia oxidation

Alloy catalysts design faces the contradiction of small sample and huge screen space, especially in rational design with multi-objective and multi-constraints. Here, we conduct the active learning enabled innovative catalyst screening in alloy space composed of transition metal elements. First, the small dataset and large search space are constructed based on knowledge informed feature group. Then, the surrogate model based on Gaussian process regression are trained for predicting catalytic activity and N2 selectivity descriptors for selective catalytic oxidation of ammonia (NH3-SCO) process, merely based on the small dataset. Furthermore, coupling pareto solution and Bayesian optimization, the active learning driven material searching are performed in the huge alloy spaces with more than 1000 configurations. After 3 iterations with high throughput calculation on 30 alloyed configurations and further theoretical validation based on microkinetic and stability analysis, 9 ensemble configurations are considered as innovative alloy catalysts of NH3-SCO with reactivity and selectivity trade-off. Our study provides the reliable framework for catalyst design with multi-objective and multi-constraints when facing with small sample data and huge searching space and gives the specific guidance for rational design of NH3−SCO alloy catalysts.

$\beta$ -wave-based exploration of sensitive EEG features and classification of situation awareness

AbstractThe purpose of this study was to explore the electroencephalogram (EEG) features sensitive to situation awareness (SA) and then classify SA levels. Forty-eight participants were recruited to complete an SA standard test based on the multi-attribute task battery (MATB) II, and the corresponding EEG data and situation awareness global assessment technology (SAGAT) scores were recorded. The population with the top 25% of SAGAT scores was selected as the high-SA level (HSL) group, and the bottom 25% was the low-SA level (LSL) group. The results showed that (1) for the relative power of $\beta$ 1 (16–20Hz), $\beta$ 2 (20–24Hz) and $\beta$ 3 (24–30Hz), repeated measures analysis of variance (ANOVA) in three brain regions (Central Central-Parietal, and Parietal) × three brain lateralities (left, midline, and right) × two SA groups (HSL and LSL) showed a significant main effect for SA groups; post hoc comparisons revealed that compared with LSL, the above features of HSL were higher. (2) for most ratio features associated with $\beta$ 1 ∼ $\beta$ 3, ANOVA also revealed a main effect for SA groups. (3) EEG features sensitive to SA were selected to classify SA levels with small-sample data based on the general supervised machine learning classifiers. Five-fold cross-validation results showed that among the models with easy interpretability, logistic regression (LR) and decision tree (DT) presented the highest accuracy (both 92%), while among the models with hard interpretability, the accuracy of random forest (RF) was 88.8%, followed by an artificial neural network (ANN) of 84%. The above results suggested that (1) the relative power of $\beta$ 1 ∼ $\beta$ 3 and their associated ratios were sensitive to changes in SA levels; (2) the general supervised machine learning models all exhibited good accuracy (greater than 75%); and (3) furthermore, LR and DT are recommended by combining the interpretability and accuracy of the models.

A combination network based on graph modules for cardiac segmentation

BackgroundCardiac segmentation plays a crucial role in extracting cardiac substructures from computed tomography images, providing necessary information for subsequent cardiac disease diagnostics. Current research on cardiac segmentation algorithms faces challenges such as complex spatial distributions and limited labeled samples. The preferred method, convolutional neural network (CNN), excels at capturing features at various levels. However, the coarse convolutional operations of CNN often neglect valuable structural information. In contrast, graph neural network (GNN) excels at capturing complex spatial relationships among nodes by aggregating messages from graphs. MethodologyIn this work, a GNN-CNN combination network (GCCN) with enhanced feature extraction by GNN is proposed for cardiac segmentation. The combination network integrates the strengths of two approaches while compensating for each other's shortcomings. Firstly, 3D CT images are transformed into graphs, whose nodes with similar feature values within a certain spatial proximity are connected. Secondly, a lightweight graph attention network (LGAT) module is proposed for aggregating the messages of constructed graphs. Thirdly, the data, resampled from the feature-enhanced graphs, is fed into the 3D ResU-Net for the final segmentation process. ResultThe proposed method achieves an average Dice score of 92.98% which is 1.84% higher than 3D ResU-Net. The average Dice score of each cardiac substructure improved, particularly for the ascending aorta, achieving 96.35%, an 8.29% improvement over 3D ResU-Net. Additionally, our study demonstrates that GCCN has the improved adaptability in handling datasets with limited samples. ConclusionIn general, GCCN allows for the extraction of richer structural information from CT images, resulting in stronger feature representation of the data. Compared to pure convolutional methods, GCCN not only enhances segmentation accuracy but also exhibits greater adaptability to small-sample data. GCCN represents an exploration of applying graph neural networks to cardiac segmentation tasks from a novel perspective.

Prediction of Ground Vibration Velocity Induced by Long Hole Blasting Using a Particle Swarm Optimization Algorithm

Obtaining accurate basic parameters for long hole blasting is challenging, and the resulting vibration damage significantly impacts key surface facilities. Predicting ground vibration velocity accurately and mitigating the harmful effects of blasting are crucial aspects of controlled blasting technology. This study focuses on the prediction of ground vibration velocity induced by underground long hole blasting tests. Utilizing the fitting equation based on the US Bureau of Mines (USBM) formula as a baseline for predicting peak particle velocity, two machine learning models suitable for small sample data, Support Vector Regression (SVR) machine and Random Forest (RF), were employed. The models were optimized using the particle swarm optimization algorithm (PSO) to predict peak particle velocity with multiple parameters specific to long hole blasting. Mean absolute error (MAE), mean Squared error (MSE), and coefficient of determination (R2) were used to assess the model predictions. Compared with the fitting equation based on the USBM model, both the Support Vector Regression (SVR) and Random Forest (RF) models accurately and effectively predict peak particle velocity, enhancing prediction accuracy and efficiency. The SVR model exhibited slightly superior predictive performance compared to the RF model.

Conditional independence collapsibility for acyclic directed mixed graph models

Collapsibility refers to the property that, when marginalizing over some variables that are not of interest from the full model, the resulting marginal model of the remaining variables is equivalent to the local model induced by the subgraph on these variables. This means that when the marginal model satisfies collapsibility, statistical inference results based on the marginal model and the local model are consistent. This has significant implications for small-sample data, modeling latent variable data, and reducing the computational complexity of statistical inference. This paper focuses on studying the conditional independence collapsibility of acyclic directed mixed graph (ADMG) models. By introducing the concept of inducing paths in ADMGs and exploring its properties, the conditional independence collapsibility of ADMGs is characterized equivalently from both graph theory and statistical perspectives.

Meta-learning-based approach for tool condition monitoring in multi-condition small sample scenarios

Tool Condition Monitoring (TCM) technology in machining is crucial for maintaining safety and optimizing costs. However, its practical application faces two significant challenges: difficulties in data collection and a decline in generalization performance across different monitoring tasks. To this end, a hybrid feature boundary-enhanced meta-learning network with adaptive gradients (HFBEAML) is proposed. This method combines cutting process parameters with time-series signal features, employing a multimodal one-dimensional Convolutional Neural Network (1D-CNN) based on the DenseNet architecture and a multi-head self-attention mechanism (MHSA) to mine multi-dimensional features sensitive to tool wear. To further enhance the model’s feature discrimination capability, a multi-loss joint optimization strategy is introduced, combining task-level loss with an improved triplet loss. This approach incorporates strategies for adaptive boundaries and handling the hardest positive and negative sample sets, thereby enhancing the robustness of feature metrics. Additionally, this research innovatively proposes an adaptive meta-level gradient update mechanism, dynamically adjusting gradient weights according to the characteristics of multiple tasks, aiming to improve the model’s generalization ability in multi-task learning environments. The effectiveness of the proposed method is demonstrated through experiments in two different scenarios, comparing its results with five other models showcasing its significant advantages in multi-task, small-sample data monitoring environments.

COMPARISON OF THE USE OF SENTINEL-1 SAR AND ALOS-2 PALSAR-2 IN MANGROVE ABOVEGROUND BIOMASS ESTIMATION IN SAN JUAN, BATANGAS, PHILIPPINES

Abstract. This study compares the potential of Sentinel-1 and ALOS-2 PALSAR-2 in estimating mangrove aboveground biomass (AGB) in San Juan, Batangas, Philippines. Mangrove forests are essential coastal ecosystems that are facing growing threats. One way of conserving them is by creating policies that can protect them. To do this effectively, information like AGB can be used as a guide. However, conventional AGB estimations are labor-intensive and ecologically disruptive. Conversely, remote sensing technologies, such as synthetic aperture radar (SAR), offer a more efficient alternative. Sentinel-1, operating in C-band, and ALOS-2 PALSAR-2, operating in L-band, are two prominent SAR platforms with global coverage, offering data for land cover classification, forest monitoring, and forest biomass estimation. This research used the backscatter values of Sentinel-1 and ALOS-2 PALSAR-2 as predictor variables in estimating mangrove AGB by correlating them to the observed AGB from a mangrove survey. The models developed using these platforms yielded limited accuracy, with low coefficient of determination (R2) (Sentinel-1 = 0.13; ALOS-2 PALSAR-2 = 0.12) and RMSE (Sentinel-1 = 8.72 Mg ha-1; ALOS-2 PALSAR-2 = 8.78 Mg ha-1). Potential sources of errors were identified, including small sample size and data noise. On the results, Sentinel-1 demonstrates a slightly better performance in terms of the R2 and RMSE in the modeling while ALOS-2 PALSAR-2 performed better in the validation, however, both still yielded suboptimal AGB estimates compared to other studies. Refining the models by incorporating additional parameters, exploring machine learning, and considering other data sources are recommended to enhance AGB estimation.

Treatment selection and real-world analysis of immunotherapy with or without chemotherapy in PD-L1-high metastatic non-small cell lung cancer.

Lung cancer is the leading cause of cancer death in Australia. Immunotherapy has improved outcomes in patients with metastatic non-small cell lung cancer (NSCLC). Pembrolizumab is approved in first-line treatment as single-agent immunotherapy (SAI) or combination chemoimmunotherapy (CIT). In metastatic NSCLC programmed death-ligand 1 (PD-L1) ≥50% either regimen may be used. We aim to identify patient and tumour characteristics that influence treatment selection. This is a retrospective observational study. Pharmacy records identified patients with metastatic/recurrent NSCLC receiving pembrolizumab at two metropolitan centres in Victoria, Australia, since 2018. Demographics, tumour characteristics, Charlson Comorbidity Index (CCI) and treatment data were collected. Descriptive and multivariate analyses were performed. Sixty-one patients had metastatic NSCLC PD-L1 ≥50% and received pembrolizumab with median age of 65.6 years, Eastern Cooperative Oncology Group 0-1 in 82%. CIT was administered to 23% (14) with no difference in rate of delivery between centres (P = 0.808). CCI mean score differed (3.38 SAI vs 2.36 CIT, P = 0.042). Patients with high CCI score (≥2) were less likely to receive CIT (OR = 0.15, P = 0.003, 95% confidence interval (CI) 0.04-0.57). Primary tumours over 5 cm were more likely to receive CIT (OR = 3.74, P = 0.043, 95% CI = 1.04-13.42). Site-specific metastases of liver, brain and pericardial effusion were not associated with CIT. Patients with higher comorbidity score were less likely to receive CIT, suggesting chemotherapy avoidance in comorbid patients. Larger tumours are associated with CIT use, indicating that oncologists may use tumour size as a surrogate of disease burden. Limitations include small sample size and data cut-off. Future prospective studies could incorporate comorbid status and a validated disease burden score to stratify patients.

Bayesian uncertainty quantification of modal parameters and RRF identification of transmission towers with limited measured vibration data

The resonant response factor (RRF) sensitive to modal parameters, including the damping ratio and frequency, is a critical parameter for wind-resistant design of extra high voltage (EHV) transmission towers, because it directly affects the calculation of the wind vibration coefficient. However, the research on operational modal analysis (OMA) of in-service EHV transmission towers is limited due to the high risk of field monitoring. Therefore, it is critical to determine the size of sufficient data samples or minimum monitoring duration for the OMA of a transmission tower. In this study, an investigation of uncertainty quantification in Bayesian OMA of EHV transmission towers with small data samples from the ambient dynamic test is carried out. The uncertainty of the resonant component factor for wind-resistance design is proposed and quantified, which could provide engineering designers with a reference for confidence levels. Firstly, a field test system is installed on a multipurpose EHV transmission tower with a closed-loop cat head and a pair of cross-arms, to gather the acceleration responses. Then, the OMA for the transmission tower is carried out by the fast Bayesian FFT (FBFFT) method to determine the modal parameters as well as the associated posterior uncertainty. The small sample analysis of OMA for the transmission tower is further performed to obtain sufficient data samples and minimum monitoring duration. Finally, the distribution of the RRF is presented with the different confidential levels. It is found that a sampling length of 600 s could fulfill the basic needs of accuracy in Bayesian OMA and the determination of RRF. The outcomes of this study may provide a reference for the wind-resistance design parameter selection of the similar type of transmission towers.

The Outliers Influence on Adequateness of Classical and Robust Path Analysis

Path analysis is formed from correlation and regression analysis which assumes a normal distribution. This assumption will be disturbed if there are outliers. This research aims to examine the influence of outliers on classical path analysis and robust path analysis. The data used as initial data is secondary data from Badan Pusat Statistik (BPS) publications on Indikator Kesejahteraan Rakyat, Statistik Ketenagakerjaan, Statistik Indonesia, and Survei Sosial Ekonomi Nasional. These data are used to generate data with a simulation scheme for the number of samples or n (20, 30, and 100), percentage of outliers or p (5%, 25% and 45%) and program repetitions or u (25, 50, 75, 100, 500 and 1000). Based on the combination of 3 treatments, the percentage of model adequateness was measured based on the Wald test and then an ANOVA test was carried out with 2-factor factorial design. The percentage of model adequateness of the classical path analysis model is decreasing as the number of samples increasing. In large sample sizes data, the adequateness tends to be different and increases as the percentage of outliers in the sample size data increases. The adequateness of the robust path analysis model is relatively very stable. The robust path analysis is adequate to use on small or large sample data with any percentage of outliers. The percentage of model adequateness being higher at the larger percentage of outliers. The classical path analysis model is influenced by outliers but the robust path analysis model is not influenced by outliers.

A method of evaluating cell state based on data augmentation and ViT16

In this paper, based on the model of data augmentation and Vision Transformer 16 (ViT16), a method of assessment for electrolysis cell state is presented to get the real-time information of the current cell state, so as to improve current efficiency of process. Firstly, in order to solve the issue of the small sample data and improve classification accuracy, the method of data augmentation is performed on the flame hole images by using convolutional block attention module to improve auxiliary classifier generativhyhee adversarial network. Secondly, the deep feature data of the flame hole images is extracted by the method of ViT16, and the genetic algorithm is applied to eliminate the redundant feature data to improve the accuracy. Thirdly, the support vector machines model is employed to classify the feature data, and the aluminum cells are classified into cold, hot, and normal. Finally, the actual data are applied to the experiments of the above method, the results of experiments show that this method is better than other methods, and the accuracy of classifying the cell state is as high as 98.677%. This is of great significance for the guidance of aluminum electrolysis production process.

Intelligent fault diagnosis of rolling bearings under small samples based on lightweight UNet with attention-fused residual block

In rotating machinery, rolling bearings are crucial, and their failure can lead to severe accidents and economic losses. Therefore, fault diagnosis of bearings is necessary to maintain the safe and stable operation of modern machinery and equipment. Currently, data-driven intelligent diagnosis methods are mainstream; however, in practical applications, problems such as insufficient fault samples and strong interference signals often exist. At the same time, a large number of edge-end and mobile devices put higher requirements for the size of the diagnostic model. This study addresses these issues by proposing a lightweight UNet (LWUNet) model, which integrates wavelet packet decomposition (WPD) and attention-fused residual block (AFRB) for fault diagnosis in rolling bearings under varying operating conditions, particularly for small sample sizes. Firstly, WPD is used to decompose and reconstruct the fault signal to achieve effective denoising. Secondly, a LW-UNet is constructed for pixel-level feature learning to reduce the number of parameters and improve the accuracy rate. Thereafter, to further enhance the model feature extraction capability, the AFRB is proposed and embedded into the LWUNet to develop the AFRB-LWUNet model. Finally, the reconstructed signals are input to the proposed model for training, and the model performance is examined using a test set. The proposed method is compared with other fault diagnosis models using small sample data of rolling bearings from the Case Western Reserve University, USA and the University of Paderborn, Germany. The results confirm the higher recognition accuracy, stronger generalization ability, and robustness of the proposed method for small samples under various working conditions and intense noise.

Assessment of computing systems reliability by non-parametric method by small samples of operational data

A new method for assessing the reliability of small computing systems that allows the generation of only small samples of operational data is proposed in the article. The result of applying the technique is the posterior failure distribution density, on the basis of which various reliability indicators can be calculated. The methodology consists of two stages: the first is the preparation of operational data, including detection of failures using machine learning methods, and the second is the construction of the failure distribution density using the adapted Rosenblatt–Parzen method. Increasing the efficiency of estimates using the proposed method is achieved by taking into account censored data, compensating for the shift of failure distribution densities and finding the optimal smoothing parameter.

Probabilistic Graph Model Based Recommendation Algorithm for Material Selection in Self-directed Learning

Faced the vast amount of information, choosing the appropriate materials is a prerequisite for effective self-directed learning. The recommendation algorithm is a kind of intelligent technology that can accurately locate the required information which the users care about most. However, many recommendation techniques experience can not be trained adequately in scenarios with small sample data and extremely sparse ratings. Moreover, DLRAs (Deep learning based Recommendation Algorithms) require high hardware support. The probabilistic graph (PG) can effectively represent the implicit complex relations among nodes, but it still has the problem of sparse data sensitivity. Therefore, we propose a Matrix-Factorization-based Probabilistic Graph Model for Recommendation Algorithm (MF-PGMRA): By matrix-factorizing the sparse rating matrix, the users and items are mapped to the user/item spaces, respectively; We employ the inner product to data-enhance and overcome the problems of sparse data and cold start; Then, we build Probabilistic Graph to construct the “user-item” latent spaces and estimate the probability distribution based on expectation maximization (EM), so as to predict the ratings; Finally, we built a library management system with the recommendation module to highlight the benefits of MF-PGMRA for students’ subject learning. According to a questionnaire, we confirmed that the students are satisfied with the system from four aspects of speed, accuracy, usability and convenience, which can confirm that the library management system based on MF-PGMRA can efficiently and accurately recommend suitable materials for students from the huge amount of learning materials to improve students’ self-directed learning efficiency.