Dimensionality reduction is widely used to visualize complex high-dimensional data. This study presents a novel method for effective data visualization. Previous methods depend on local distance measurements for data manifold approximation. This leads to unreliable results when a data manifold locally oscillates because of some undesirable effects, such as noise effects. In this study, we overcome this limitation by introducing a dual approximation of a data manifold. We roughly approximate a data manifold with a neighborhood graph and prune it with a global filter. This dual scheme results in local oscillation robustness and yields effective visualization with explicit global preservation. We consider a global filter based on principal component analysis frameworks and derive it with the spectral information of the original high-dimensional data. Finally, we experiment with multiple datasets to verify our method, compare its performance to that of state-of-the-art methods, and confirm the effectiveness of our novelty and results.

Dimensionality reduction plays an important role in interpreting and visualizing high-dimensional data. Previous methods for data visualization overestimate the local structure and lack the consideration of global preservation. In this study, we develop a Gaussian process latent variable model (GP-LVM) for data visualization. GP-LVMs are one of the frameworks of principal component analysis and preserve the global structure effectively. The drawbacks of GP-LVMs are the absence of local structure preservation and the use of low-expressive kernel functions. Therefore, we introduce regularization for local preservation and an expressive kernel function into GP-LVMs to overcome these limitations. As a result, we reflect the global and local structures in low-dimensional representations, improving the reliability and visibility of embeddings. We conduct qualitative and quantitative experiments comparing baselines and state-of-the-art methods on image and text datasets.

Neighbor embedding is widely employed to visualize high-dimensional data; however, it frequently overlooks the global structure, e.g., intercluster similarities, thereby impeding accurate visualization. To address this problem, this paper presents Star-attracted Manifold Approximation and Projection (StarMAP), which incorporates the advantage of principal component analysis (PCA) in neighbor embedding. Inspired by the property of PCA embedding, which can be viewed as the largest shadow of the data, StarMAP introduces the concept of \textit{star attraction} by leveraging the PCA embedding. This approach yields faithful global structure preservation while maintaining the interpretability and computational efficiency of neighbor embedding. StarMAP was compared with existing methods in the visualization tasks of toy datasets, single-cell RNA sequencing data, and deep representation. The experimental results show that StarMAP is simple but effective in realizing faithful visualizations.

This study aims to accurately predict students’ academic performance trajectories for university entrance examinations by proposing a machine learning framework that explicitly accounts for missing data and uncertainty. Mock examination data are characterized by substantial missing values due to heterogeneous participation in exams, as well as inherent randomness caused by variations in test content and examinee conditions. Conventional single-value imputation methods cannot adequately reconstruct the missing values arising from such heterogeneous participation without introducing strong bias, and existing educational prediction models based on deterministic formulations do not account for the inherent randomness and uncertainty in examination scores, thereby limiting the reliability of their forecasts. To address these challenges, we employ GP-VAE and SAITS, state-of-the-art methods for time-series imputation, to reconstruct incomplete mock examination data. Furthermore, we develop a Bayesian Neural Network (BayesNN) to predict future academic performance while explicitly modeling uncertainty. By integrating temporally aware imputation with probabilistic prediction, the proposed framework aims to provide more accurate and reliable performance forecasts than existing approaches. We evaluate the effectiveness of the proposed method through comparative experiments involving various combinations of imputation techniques and prediction models. Experimental results demonstrate that the proposed framework achieves competitive predictive accuracy: the combination of deep imputation methods and BayesNN yields the lowest average estimation error of 15.98 points, compared with 16.75 points for the conventional combination of mean imputation and linear regression. The contribution of this study does not lie in proposing a new deep learning model itself, but rather in systematically comparing combinations of time-series imputation methods and uncertainty-aware prediction models using real-world mock examination sequence data with missing values, thereby providing effective design guidelines for educational data analysis.