Dimensionality Reduction Method Research Articles

A method for predicting photovoltaic output power based on PCC-GRA-PCA meteorological elements dimensionality reduction method

ABSTRACT Photovoltaic (PV) power generation forecasting models require a large amount of meteorological data, which may include irrelevant and redundant information. As the volume of data increases, the dataset is likely to contain a significant amount of irrelevant and redundant information. This paper proposes a method for reducing dimensionality based on PCC-GRA-PCA method, which aims to simplify the model and reduce computational complexity. Firstly, the dimension reduction method analyzes the feature importance of various meteorological elements by using Pearson Correlation Coefficient (PCC) and Grey Relation Analysis (GRA), which can achieve the preliminary dimension reduction of data by selecting the most relevant features. Next, the data is processed using Principal Component Analysis (PCA) to achieve a secondary dimension reduction of meteorological data through feature transformation. Finally, a photovoltaic power prediction model has been established using the OVMD-tSSA-LSSVM algorithm. After analysis, it was found that the prediction model showed improvements in R2, MAE, RMSE, and MAPE after PCC-GRA-PCA dimensionality reduction compared to the prediction model before dimensionality reduction, as well as the prediction model after LDA and PCA dimensionality reduction. This demonstrates the effectiveness of reducing data dimensionality.

Convolutional Dimension-Reduction With Knowledge Reasoning for Reliability Approximations of Structures Under High-Dimensional Spatial Uncertainties

Abstract Along with the rapid advancement of additive manufacturing technology, 3D-printed structures and materials have been successfully employed in various applications. Computer simulations of these structures and materials are often characterized by a vast number of spatial-varied parameters to predict the structural response of interest. Direct Monte Carlo methods are infeasible for uncertainty quantification and reliability assessment of such systems as they require a large number of forward model evaluations to obtain convergent statistics. To alleviate this difficulty, this paper presents a convolutional dimension-reduction method with knowledge reasoning-based loss regularization for surrogate modeling and uncertainty quantification of structures with high-dimensional spatial uncertainties. To manage the inherent high-dimensionality, a deep convolutional dimension-reduction network (ConvDR) is constructed to transform the spatial data into a low-dimensional latent space. In the latent space, knowledge reasoning is formulated as a form of loss regularization, and evolutionary algorithms are employed to train both the ConvDR network and a linear regression model as surrogate models for predicting the response of interest. 2D structures with spatial-variated material compositions are used to demonstrate the performance of the proposed approach.

Genetic association study of TERT gene variants with chronic kidney disease susceptibility in the Chinese population

The incidence and mortality of chronic kidney disease (CKD) are increasing globally. Studies have demonstrated the significance of genetic risk factors in the progression of CKD. Telomerase reverse transcriptase (TERT) may be implicated in the development of CKD. This study aimed to investigate the correlation between TERT gene variants and susceptibility to CKD in the Chinese population. A total of 507 patients with CKD and 510 healthy controls were recruited for this case-control study. Four candidate loci were identified using the MassARRAY platform. Logistic regression analysis was employed to assess the association between TERT gene variants and the risk of CKD. The false positive reporting probability (FPRP) method was utilized to evaluate the validity of statistically significant associations. The multifactorial dimensionality reduction (MDR) method was used to evaluate the interaction between SNPs and the risk of CKD. Furthermore, discrepancies in the clinical features of subjects with diverse genotypes were evaluated using one-way analysis of variance (ANOVA). Our findings revealed a correlation between rs2735940 and rs4635969 and an increased risk of CKD. Stratification analysis indicated that rs4635969 was related to an increased risk of CKD in different subgroups (age ≤ 50 years and male). MDR analysis indicated that the two-site model (rs2735940 and rs4635969) was the best prediction model. Furthermore, the rs2735940 GG genotype was found to be linked to an increased level of microalbuminuria (MAU) in patients with CKD. Our study is the first to reveal a connection between TERT gene variants and susceptibility to CKD, providing new insights into the field of nephrology.

Association between PRKG1 gene and gene-environment interactions with pediatric asthma

Objective To investigate the relationship between single nucleotide polymorphisms (SNPs) of cGMP-dependent protein kinase I (PRKG1) gene and gene-environment interactions with bronchial asthma in children. Methods 109 asthma patients and 158 healthy controls from the General Hospital of Northern Theater Command were enrolled, based case–control study. The iMLDR® multiple SNP typing technique was applied to detect the genotypes of rs7903366, rs7081864, rs7070958 and rs7897633 in PRKG1 gene. The percentage of eosinophils (EOS%) in peripheral blood and serum immunoglobulin E (IgE) in the case group were also measured. Gene-environment interactions were examined using the generalized multi-factor dimensionality reduction (GMDR) method. Results There were polymorphisms in four SNPs of PRKG1 gene in the case and control groups. The genotype and allele frequencies distribution of rs7897633 demonstrated statistical significance (p < 0.05). There were no statistically significant differences in EOS% and IgE among genotypes at the four SNPs of PRKG1 gene (p > 0.05). The haplotypes CAGA and TGAC presented significant association with asthma risk (p < 0.05). The four-factor model indicated a potential gene-environment interaction in rs7897633, allergen exposure, residence, and environmental tobacco smoke (ETS) exposure (p < 0.05). Conclusions The rs7897633 in PRKG1 gene was associated with susceptibility to childhood asthma, and C allele is a protective factor. The haplotype CAGA had a protective effect against asthma risk and TGAC was linked to the high risk of developing asthma. Moreover, the interaction of rs7897633, allergen exposure, residence, and ETS exposure conferred susceptibility to childhood asthma.

NPCA: a linear dimensionality reduction method using a multilayer perceptron.

Background: Linear dimensionality reduction techniques are widely used in many applications. The goal of dimensionality reduction is to eliminate the noise of data and extract the main features of data. Several dimension reduction methods have been developed, such as linear-based principal component analysis (PCA), nonlinear-based t-distributed stochastic neighbor embedding (t-SNE), and deep-learning-based autoencoder (AE). However, PCA only determines the projection direction with the highest variance, t-SNE is sometimes only suitable for visualization, and AE and nonlinear methods discard the linear projection. Results: To retain the linear projection of raw data and generate a better result of dimension reduction either for visualization or downstream analysis, we present neural principal component analysis (nPCA), an unsupervised deep learning approach capable of retaining richer information of raw data as a promising improvement to PCA. To evaluate the performance of the nPCA algorithm, we compare the performance of 10 public datasets and 6 single-cell RNA sequencing (scRNA-seq) datasets of the pancreas, benchmarking our method with other classic linear dimensionality reduction methods. Conclusion: We concluded that the nPCA method is a competitive alternative method for dimensionality reduction tasks.

Optimizing feature subset for schizophrenia detection using multichannel EEG signals and rough set theory.

Schizophrenia (SZ) is a mental disorder that causes lifelong disorders based on delusions, cognitive deficits, and hallucinations. By visual assessment, SZ diagnosis is time-consuming and complicated, because brain states are more effectively revealed by electroencephalogram (EEG) signals, which are effectively used in SZ diagnosis. The application of existing deep learning methods in SZ detection is effective in the classification of 2-dimensional images, and these methods require more computational resources. Therefore, dimensionality reduction is necessary for SZ diagnosis using EEG signals. To reduce the dimensionality of the data, an improved CAO (ICAO) dimensionality reduction method is proposed, which integrates horizontal and vertical crossover approaches with AOA. The optimal feature subset is achieved by satisfying the ICAO conditions, and a fitness function is evaluated based on rough sets for improved accuracy in feature selection. Therefore a Crossover-boosted Archimedes optimization algorithm (AOA) with rough sets for Schizophrenia detection (CAORS-SD) was proposed using multichannel EEG signals from both SZ and normal patients. The signals are decomposed using multivariate empirical mode decomposition into multivariate intrinsic mode functions (MIMFs). Entropy metrics such as spectral entropy, permutation entropy, approximate entropy, sample entropy, and SVD entropy are evaluated on the MIMF domain to detect SZ. The processing time of the kernel support vector machine classifier is minimized with fewer features, reducing the risk Fof overfitting. Accuracy, sensitivity, specificity, precision, and F1-score of the CAORS-SD model should be conducted to diagnose SZ. Therefore, the proposed CAORS-SD method achieves the higher performance of accuracy, sensitivity, specificity, precision, and F1-score values of 96.34, 98.95, 96.86, 98.52, and 96.74% respectively. Also, the CAORS-SD method minimizes the error rate and significantly reduces the execution time.

High-performance soil class delineation via UMAP coupled with machine learning in Kurdistan Province, Iran

In response to the demand for spatial information on the soil to support the sustainable management of soil resources, this study applies a digital soil mapping approach to predict soil classes for a 7000 ha area, located in Kurdistan province, Iran. Based on a stratified random sampling design, 91 soil profiles were situated, described, and classified into soil great groups. Environmental covariates used for modelling soil classes included terrain derivatives, remote sensing data, distance-based rasters, and legacy geospatial information (e.g., geological map). To address the issue of data multi-collinearity among the predictors, three dimensionality reduction techniques were tested: the principal component analysis (PCA), t-distributed stochastic neighbor embedding (t-SNE), and the novel Uniform Manifold Approximation and Projection (UMAP). An initial suite of 160 environmental covariates was reduced to 10 for all the methods and used to train a Random Forest (RF) model. The most effective model coupled UMAP with the Random Forest (RF-UMAP) machine-learner, which yielded a kappa index and overall accuracy values of 0.73 and 0.80, respectively. Within Kurdistan, topography and parent material were the main soil-forming factors influencing the prediction of the soil classes. Overall, the use of UMAP outperformed PCA and t-SNE. This study demonstrates the value of using advanced dimension reduction methods to facilitate the handling of non-linear relationships among predictor variables when using RF.

Association of SOX6 gene polymorphisms with Kashin-Beck disease risk in the Chinese Han population.

Kashin-Beck disease (KBD) is an endemic osteochondropathy. A specific gene called SRY-box transcription factor 6 (SOX6) is important for forming cartilage. This study aims to explore the potential correlation between SOX6 single nucleotide polymorphisms (SNPs) and KBD risk for the first time. In the case-control study, 735 unrelated Chinese Han individuals were enrolled. The four mutation sites of the SOX6 gene (rs4539287 G/A, rs3203295 C/A, rs7928675 C/A, and rs10832681 A/G) were screened and genotyped on the Agena MassARRAY platform. The correlation between SOX6 SNPs and KBD risk was explored based on logistic regression analysis. The interaction between SNP and SNP was analyzed based on the multi-factor dimensionality reduction (MDR) method. Overall analysis revealed a remarkable correlation between rs7928675 and rs10832681 and the reduction of KBD risk (p < 0.05). Subgroup analyses further indicated that these two SNPs have a significant protective effect on KBD risk among participants aged ≤65 years, males, and non-smokers (p < 0.05). MDR displayed a marked interaction between rs3203295 and rs10832681. Our study revealed that SOX6 rs7928675 and rs10832681 are markedly correlated with a reduced risk of KBD in the Chinese Han population, providing a new direction for the prevention, diagnosis, and treatment of KBD.

Evergene: an interactive webtool for large-scale gene-centric analysis of primary tumours.

The data sharing of large comprehensive cancer research projects, such as The Cancer Genome Atlas (TCGA), has improved the availability of high-quality data to research labs around the world. However, due to the volume and inherent complexity of high-throughput omics data, analysis of this is limited by the capacity for performing data processing through programming languages such as R or Python. Existing webtools lack functionality that supports large-scale analysis; typically, users can only input one gene, or a gene list condensed into a gene set, instead of individual gene-level analysis. Furthermore, analysis results are usually displayed without other sample-level molecular or clinical annotations. To address these gaps in the existing webtools, we have developed Evergene using R and Shiny. Evergene is a user-friendly webtool that utilizes RNA-sequencing data, alongside other sample and clinical annotation, for large-scale gene-centric analysis, including principal component analysis (PCA), survival analysis (SA), and correlation analysis (CA). Moreover, Evergene achieves in-depth analysis of cancer transcriptomic data which can be explored through dimensional reduction methods, relating gene expression with clinical events or other sample information, such as ethnicity, histological classification, and molecular indices. Lastly, users can upload custom data to Evergene for analysis. Evergene webtool is available at https://bshihlab.shinyapps.io/evergene/. The source code and example user input dataset are available at https://github.com/bshihlab/evergene.

Functional PCA and deep neural networks-based Bayesian inverse uncertainty quantification with transient experimental data

This work focuses on developing an inverse uncertainty quantification (IUQ) process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the IUQ of TRACE physical model parameters using the FEBA benchmark transient experimental data on peak cladding temperatures during reflooding. The quantity-of-interest (QoI) is time-dependent peak cladding temperature (PCT) profiles. Conventional PCA can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information in the PCT profiles before conventional PCA is applied for dimensionality reduction. The resulting PC scores are then used to build DNN-based surrogate models to significantly reduce the computational cost in Markov Chain Monte Carlo sampling, while the code/interpolation uncertainty is accounted for using Bayesian neural networks. We compared four IUQ processes with different dimensionality reduction methods and surrogate models. The proposed approach has demonstrated the best performance in reducing the dimensionality of the transient PCT profiles. This approach also produces the posterior distributions of the physical model parameters with which the model predictions have the best agreement with the experimental data.

Novel dimensionality reduction method, Taelcore, enhances lung transplantation risk prediction

In this work, we present a new approach to predict the risk of acute cellular rejection (ACR) after lung transplantation by using machine learning algorithms, such as Multilayer Perceptron (MLP) or Autoencoder (AE), and combining them with topological data analysis (TDA) tools. Our proposed method, named topological autoencoder with best linear combination for optimal reduction of embeddings (Taelcore), effectively reduces the dimensionality of high-dimensional datasets and yields better results compared to other models. We validate the effectiveness of Taelcore in reducing the prediction error rate on four datasets. Furthermore, we demonstrate that Taelcore’s topological improvements have a positive effect on the majority of the machine learning algorithms used. By providing a new way to diagnose patients and detect complications early, this work contributes to improved clinical outcomes in lung transplantation.

Ship Engine Model Selection by Applying Machine Learning Classification Techniques Using Imputation and Dimensionality Reduction

The maritime is facing a gradual proliferation of data, which is frequently coupled with the presence of subpar information that contains missing and duplicate data, erroneous records, and flawed entries as a result of human intervention or a lack of access to sensitive and important collaborative information. Data limitations and restrictions have a crucial impact on inefficient data-driven decisions, leading to decreased productivity, augmented operating expenses, and the consequent substantial decline in a competitive edge. The missing or inadequate presentation of significant information, such as the vessel’s primary engine model, critically affects its capabilities and operating expenses as well as its environmental impact. In this study, a comprehensive study was employed, using and comparing several machine learning classification techniques to classify a ship’s main engine model, along with different imputation methods for handling the missing values and dimensionality reduction methods. The classification is based on the technical and operational characteristics of the vessel, including the physical dimensions, various capacities, speeds and consumption. Briefly, three dimensionality reduction methods (Principal Component Analysis, Uniform Manifold Approximation and Projection, and t-Distributed Stochastic Neighbor Embedding) were considered and combined with a variety of classifiers and the appropriate parameters of the dimensionality reduction methods. According to the classification results, the ExtraTreeClassifier with PCA with 4 components, the ExtraTreeClassifier with t-SNE with perplexity equal to 10 and 3 components, and the same classifier with UMAP with 10 neighbors and 3 components outperformed the rest of the combinations. This classification could provide significant information for shipowners to enhance the vessel’s operation by optimizing it.

Carbon price prediction based on a scaled PCA approach.

Carbon price prediction is of great importance to regulators and participants in the carbon trading market. It is the basis for developing policies related to the carbon trading market and stabilizing that market. Considering the numerous factors that influence carbon prices in China, dimensionality reduction is needed to improve the prediction accuracy and efficiency. However, the traditional dimensionality reduction methods fail to fully consider the role of influencing factors, which has certain limitations. In this paper, a new dimensionality reduction method, namely scaled principal component analysis (s-PCA), is employed to improve the prediction accuracy of carbon prices. Firstly, a factor library that influence carbon prices is constructed from three perspectives: technical indicators, financial indicators and commodities indicators. Then, the s-PCA method is used to reduce the dimensionality of factors influencing carbon price. Next, two different methods are used to predict carbon prices, including traditional regression method and Long Short-Term Memory (LSTM) method. Finally, the economic value of the s-PCA method is examined by constructing investment portfolios. The empirical results of the Hubei Emissions Exchange show that the s-PCA model outperforms other competing models both in- and out-of-sample. In addition, the LSTM model could improve the performance of the s-PCA model in carbon price prediction. From a market timing perspective, investors can achieve a greater return and a larger Sharpe ratio using the s-PCA method than using other comparative methods and buy-and-hold strategy. Therefore, the s-PCA method is effective and robust in predicting carbon price.

Neighbor-based joint spatial division and multiplexing in massive MIMO: user scheduling and dynamic beam allocation

AbstractTwo-stage precoding schemes have been developed to reduce the channel estimation overhead in FDD systems. By integrating user scheduling into these schemes, it becomes possible to meet the quality-of-service requirements of high-density wireless communication systems, despite the limitations on spatial resources and transmit power budget. In this paper, we propose a user scheduling and dynamic beam allocation method for neighbor-based joint spatial division multiplexing (N-JSDM) transmission. The user scheduling problem is formulated as a 0–1 quadratic programming problem to maximize effective spectral efficiency (ESE) using directional channel properties. To address the complexity issue, convex relaxation and linearization methods are employed to transform the problem into a 0–1 mixed integer linear programming, and a dimensionality reduction method is introduced. The proposed user scheduling-aided N-JSDM scheme reduces downlink training length and feedback of channel state information. Additionally, a dynamic configuration form is used for pre-beamforming matrix design based on user distribution, outperforming conventional approaches. Simulation results demonstrate higher ESE achieved by the proposed scheme compared to previous methods.

A Fusion Dimension Reduction Method for the Features of Surface Electromyographic Signals.

Surface electromyographic signals (sEMG) usually have high-dimensional properties, and direct processing of these data consumes significant computational resources. Dimensionality reduction processing can reduce the dimension of the data and improve the real-time performance and response speed. This is especially important for application scenarios such as prosthetic control and rehabilitation training where rapid feedback is required. This paper proposes a feature fusion dimension reduction method for sEMG signals. This method is constructed based on the unique correlation between the features of sEMG. To test the performance of the new dimension reduction method, the sEMG signals from five leg movements were collected from eight subjects and the classification of the feature matrix before and after dimension reduction was tested by six classifiers. The results show that the feature matrix after fusion dimension reduction has excellent classification performance in the subsequent classification tasks. It produces up to 98.3% accuracy. And the highest comprehensive evaluation index can reach 0.9958. This paper also compares the new method with three commonly used dimensionality reduction methods. The results show that the performance of the new method is not only optimal but also extremely stable. Because its classification performance will not be lower than other dimensionality reduction methods due to the change of classifiers. This confirms that the new method has a higher utility value in sEMG signals processing compared to other dimension reduction methods.

Toward Robust Discriminative Projections Learning Against Adversarial Patch Attacks.

As one of the most popular supervised dimensionality reduction methods, linear discriminant analysis (LDA) has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the ratio of squared l2 norms, which is vulnerable to the adversarial examples. In recent studies, many l1 -norm-based robust dimensionality reduction methods are proposed to improve the robustness of model. However, due to the difficulty of l1 -norm ratio optimization and weakness on defending a large number of adversarial examples, so far, scarce works have been proposed to utilize sparsity-inducing norms for LDA objective. In this article, we propose a novel robust discriminative projections learning (rDPL) method based on the l1,2 -norm trace-ratio minimization optimization algorithm. Minimizing the l1,2 -norm ratio problem directly is a much more challenging problem than the traditional methods, and there is no existing optimization algorithm to solve such nonsmooth terms ratio problem. We derive a new efficient algorithm to solve this challenging problem and provide a theoretical analysis on the convergence of our algorithm. The proposed algorithm is easy to implement and converges fast in practice. Extensive experiments on both synthetic data and several real benchmark datasets show the effectiveness of the proposed method on defending the adversarial patch attack by comparison with many state-of-the-art robust dimensionality reduction methods.

A New Hyperspectral Image Identification Method Based on LSDA and OSELM

To solve the problems of information loss and nonlinear transformation of hyperspectral image dimensionality reduction methods and the problem that recognition methods are sensitive to noise and cannot be trained online, a new hyperspectral image identification method based on locality sensitive discriminant analysis (LSDA) and online sequential extreme learning machine (OSELM) is proposed. Firstly, LSDA is used to reduce the redundant information and data noise, and the local structure and discriminant information of the hyperspectral image are extracted on the basis of reducing the data dimension. Then, a real‐time recognition model based on OSELM is constructed to identify various terrain targets in hyperspectral images through online real‐time updates of data. According to the experimental results of the Pavia University dataset and Salinas dataset, the proposed LSDA‐OSELM not only achieved the maximum overall accuracy (OA) of 97.56 and 97.88 but also obtained the maximum kappa coefficient of 0.9726 and 0.9774. Compared with several new dimensionality reduction methods and identification methods, the proposed LSDA‐OSELM has achieved a leading position in both OA and kappa indicators. The proposed method improves the generalization ability and accuracy of hyperspectral image target recognition models. In the future, its computational complexity and parameter robustness are expected to be further improved and applied in practical application scenarios.

МЕТОДИ ТА МОДЕЛІ DATA SCIENCE В СУЧАСНІЙ ЕКОНОМІЦІ

In contemporary economics, data science models play a crucial role in analyzing complex relationships, predicting economic trends, and informing policy decisions. This article reviews the most commonly used data science models in economics, including econometric models like linear and logistic regression, Probit and Tobit models, time series analysis models such as ARIMA and Vector Autoregression (VAR), and panel data analysis methods like fixed and random effects models and Difference-in-Differences (DiD). Additionally, it explores machine learning algorithms, clustering and classification techniques, dimensionality reduction methods, Bayesian methods, and natural language processing (NLP) applications. The article highlights their purposes, applications, and relevant works, emphasizing the strengths and limitations of each model. It also discusses the impact of these models across various sectors, including finance, retail, energy, and healthcare. This comprehensive overview underscores the importance of aligning data science models with business objectives, ensuring data quality, investing in scalable technologies, fostering a data-driven culture, and addressing ethical considerations. The article concludes with future research directions, such as advanced neural network architectures, large language models, generative AI models, hybrid models, and the need for interpretable and ethical AI applications in economics. The importance of this topic lies in the transformative potential of data science models to enhance economic analysis and decision-making. By leveraging advanced data science techniques, economists can gain deeper insights into complex economic phenomena, improve forecasting accuracy, and develop more effective policies. As data-driven approaches continue to evolve, they provide powerful tools for addressing critical economic challenges, driving innovation, and fostering sustainable growth across various sectors.

ModalChorus: Visual Probing and Alignment of Multi-modal Embeddings via Modal Fusion Map.

Multi-modal embeddings form the foundation for vision-language models, such as CLIP embeddings, the most widely used text-image embeddings. However, these embeddings are vulnerable to subtle misalignment of cross-modal features, resulting in decreased model performance and diminished generalization. To address this problem, we design ModalChorus, an interactive system for visual probing and alignment of multi-modal embeddings. ModalChorus primarily offers a two-stage process: 1) embedding probing with Modal Fusion Map (MFM), a novel parametric dimensionality reduction method that integrates both metric and nonmetric objectives to enhance modality fusion; and 2) embedding alignment that allows users to interactively articulate intentions for both point-set and set-set alignments. Quantitative and qualitative comparisons for CLIP embeddings with existing dimensionality reduction (e.g., t-SNE and MDS) and data fusion (e.g., data context map) methods demonstrate the advantages of MFM in showcasing cross-modal features over common vision-language datasets. Case studies reveal that ModalChorus can facilitate intuitive discovery of misalignment and efficient re-alignment in scenarios ranging from zero-shot classification to cross-modal retrieval and generation.

GenURL: A General Framework for Unsupervised Representation Learning.

Unsupervised representation learning (URL) that learns compact embeddings of high-dimensional data without supervision has achieved remarkable progress recently. However, the development of URLs for different requirements is independent, which limits the generalization of the algorithms, especially prohibitive as the number of tasks grows. For example, dimension reduction (DR) methods, t-SNE and UMAP, optimize pairwise data relationships by preserving the global geometric structure, while self-supervised learning, SimCLR and BYOL, focuses on mining the local statistics of instances under specific augmentations. To address this dilemma, we summarize and propose a unified similarity-based URL framework, GenURL, which can adapt to various URL tasks smoothly. In this article, we regard URL tasks as different implicit constraints on the data geometric structure that help to seek optimal low-dimensional representations that boil down to data structural modeling (DSM) and low-dimensional transformation (LDT). Specifically, DSM provides a structure-based submodule to describe the global structures, and LDT learns compact low-dimensional embeddings with given pretext tasks. Moreover, an objective function, general Kullback-Leibler (GKL) divergence, is proposed to connect DSM and LDT naturally. Comprehensive experiments demonstrate that GenURL achieves consistent state-of-the-art performance in self-supervised visual learning, unsupervised knowledge distillation (KD), graph embeddings (GEs), and DR.