ABSTRACT Uniform Manifold Approximation and Projection (UMAP) is a prominent dimensionality reduction and visualisation algorithm that has been widely adopted in the medical and biological fields. UMAP excels at capturing complex nonlinear relationships between high‐dimensional and low‐dimensional manifolds; however, it inherently suffers from the Out‐of‐Sample embedding problem, which prevents it from directly projecting new, unseen samples onto a previously learned manifold . In this paper, we propose Kernel Uniform Manifold Approximation and Projection (KUMAP) , a kernel‐based extension designed to address this limitation. KUMAP maps training samples into a kernel space and learns the nonlinear mapping between this space and the low‐dimensional embedding. Consequently, real‐time dimensionality reduction for new samples is achieved through their projection into the kernel space. Furthermore, to leverage available label information, we introduce Supervised Kernel Uniform Manifold Approximation and Projection (SKUMAP) . Given that medical image analysis is critical for clinical diagnosis, dimensionality reduction techniques are essential for extracting key features to support intelligent decision‐making. In this study, we evaluate the KUMAP and SKUMAP algorithms across eight medical image datasets to assess their effectiveness in resolving the Out‐of‐Sample embedding problem and extracting meaningful features. Experimental results demonstrate that KUMAP and SKUMAP successfully overcome the inherent limitations of UMAP while efficiently extracting essential features from complex medical imagery.

EEG signals contain valuable physiological and psychological information, essential for brain-computer interfaces (BCIs) and neurorehabilitation. However, the non-stationarity and subject-specific variability of EEG make cross-subject generalization difficult, limiting practical deployment without costly recalibration. Unsupervised domain adaptation (UDA) aims to reduce domain discrepancies for better generalization. While many UDA methods use discrepancy-based or adversarial strategies to extract domain-invariant features, they are limited by Euclidean space, which doesn't capture EEG's nonlinear relationships. To address this, we propose a novel UDA framework on the Riemannian manifold of SPD matrices, using adversarial training. Our approach features a dual flow architecture with separate feature extractors for the source and target domains, incorporating a manifold soft parameter sharing mechanism and multi-level alignment loss for better domain alignment and feature separability. Unlike traditional methods, our model preserves domain-specific structures while aligning the feature extractors' outputs, capturing more effective domain-invariant information. Experiments on three BCI datasets show that our method outperforms several state-of-the-art UDA approaches in cross-subject EEG classification.

The functional connectivity matrix of the brain is a commonly used representation for modeling collaborative relationships of neural activity between brain regions, widely applied in research on autism spectrum disorder. This matrix is a symmetric positive semidefinite matrix, including complex non-Euclidean geometric structures. Traditional methods based on Euclidean space struggle to fully capture its intrinsic geometric relationships, limiting further improvements in model performance. In addition, previous methods still have shortcomings in selecting key connections and compressing redundant information. Based on these issues, this paper proposes a Riemannian manifold sparse Siamese autoencoder (R-SSAE): (1) This method integrates a stacked autoencoder based on SPDNet to extract deep discriminative features from the functional connectivity matrix on the Symmetric Positive Definite manifold; (2) It introduces a structured sparse regularization mechanism on the symmetric positive definite manifold to enhance critical connection identification capabilities and improve model robustness; and (3) By incorporating the Siamese network, it effectively captures subtle individual differences. Experimental results on the ABIDE dataset demonstrate that R-SSAE outperforms existing Euclidean-based and manifold learning methods in key metrics such as accuracy$(75.33 \%)$, precision$(75.44 \%)$, F1 score (73.50 %), and AUC (80.01 %), exhibiting superior discriminative capability and robustness.

In the realm of complex industrial fault diagnosis, convolutional neural network (CNN) have been widely adopted owing to their powerful feature extraction capabilities. Nevertheless, conventional two-dimensional CNN architectures often struggle to effectively capture temporal characteristics when processing grayscale images converted from time-series signals. To address this limitation, this study proposes a dual-branch network architecture that integrates one-dimensional and two-dimensional convolutional operations. Specifically, the 1D CNN branch extracts temporal features directly from raw vibration signals, while the 2D CNN branch processes grayscale images obtained through time-frequency transformation, thereby enabling a synergistic extraction of temporal and spatial representations. Moreover, to overcome the inherent limitations of traditional cascade forest approaches, we introduce a multi-classifier cascade framework based on XGBoost. By incorporating two XGBoost classifiers, the framework enhances both classification accuracy and model robustness. Empirical results indicate that the proposed model consistently achieves higher diagnostic accuracy and superior generalization performance across multiple fault datasets, particularly in bearing fault diagnosis tasks, rendering it highly suitable for deployment in complex industrial environments.

In contemporary industry, fault diagnosis is essential for detecting equipment health status and ensuring normal equipment operation. Currently, the application of the feedforward convolutional neural network method has been embraced in fault diagnosis, revealing substantial potential. A notable example of this is the PCANet. However, PCA is a linear method, which assumes the data has a global linear structure or is linearly separable. But the signal data from mechanical equipment is more of a nonlinear structure in the high-dimensional space and PCA cannot well represent the complex data and even lose some information. To address this issue, based on PCANet, a local structure-based Convolutional neural network, named LPPNet, is proposed by using locality preserving projection (LPP) to learn the convolutional filter of CNN. Because LPP can deal with complex nonlinear data and maintain the local structure of the data, more representative features can be obtained when it is used to calculate the convolution filter. This method is evaluated with the comprehensive experiments about fault diagnosis. The experiments show that LPPNet achieves a lower detection error rate compared to PCANet and some representative methods, which can be beneficial for practical applications.

The use of covariance matrices to represent an image set as data on the symmetric positive-definite (SPD) manifold has attracted widespread attention in visual classification tasks. Although numerous frameworks for SPD deep networks have emerged so far, the involvement of Riemannian gradient transformations in the backpropagation of Riemannian networks leads to slow training speeds. This has led to the lightweight manifold network SymNet. SymNet achieves relatively excellent classification performance by learning network filters using the unsupervised learning algorithm (2-D)2PCA, but this approach only considers the global structure of the data. Therefore, in this paper, we propose a simple SPD manifold deep learning network (GLSymNet) for image set classification, which introduces Locality Preserving Projections (LPP) on the SPD manifold to supplement local structural information. Specifically, in the first stage, we use (2-D)2PCA to perform initial learning on the manifold data. In the second stage, we employ a local window mechanism of SPD to partition sub-manifolds, focusing on the regional covariance information of the data and reducing the dimensionality to accelerate the training process of the network. Additionally, we use (2-D)2PCA and Lie LPP to learn filters from both global and local structures, thereby obtaining complementary feature information. We then use tangent space pooling to further reduce the dimensionality of the manifold, obtaining a more compact representation. In the output stage, we combine Kernel Discriminant Analysis (KDA) with the vectorized feature representation for discriminative subspace learning. Experiments were conducted on three typical visual classification tasks and compared with state-of-the-art methods, demonstrating the feasibility and effectiveness of the proposed GLSymNet method.

In the field of brain–computer interfaces (BCIs), the recognition of electroencephalogram (EEG) signals lies at the heart of decoding neural activity patterns and facilitating efficient human–machine interaction. Geometric learning (GL) methods have garnered increasing attention due to their enhanced robustness in EEG signal decoding. However, existing GL methods lack the ability to extract multi-scale features and spatial and channel attention from manifold data. To address these two issues, this paper proposes a model called Riemannian multi-scale residual network (RMS-RestNet), which is built upon the MAtt. RMS-RestNet designed a Riemannian multi-scale residual module (RMSRM), which extends depthwise and pointwise convolutions to the space of symmetric positive definite (SPD) manifolds, referred to as SPD depthwise (SPD DW) and SPD pointwise (SPD PW) convolutions, respectively. By employing SPD convolution kernels of varying scales, the model facilitates more comprehensive and discriminative extraction of geometric features. On this basis, residual connections are employed to fuse the geometric information of the data before and after processing, thereby enhancing the feature representation ability of the module. In addition, by combining a tangent space pooling strategy with SPD convolutions, we construct a manifold convolutional block attention module (MCBA) to capture both channel-wise and spatial attention across multi-channel SPD manifold data. Extensive experiments on both temporally synchronous and asynchronous EEG datasets demonstrate the superiority of our approach over state-of-the-art methods.

In recent years, with the rapid development of information technology, the volume of image data has grown exponentially. However, these datasets typically contain a large amount of redundant information. To extract effective features and reduce redundancy from images, a representation learning method based on the Vision Transformer (ViT) has been proposed, and to our best knowledge, Transformer was first applied to zero-shot learning (ZSL). The method adopts a symmetric encoder–decoder structure, where the encoder incorporates Multi-Head Self-Attention (MSA) mechanism of ViT to reduce the dimensionality of image features, eliminate redundant information, and decrease computational burden. Consequently, it effectively extracts features, and the decoder is utilized for reconstructing image data. We evaluated the representation learning capability of the proposed method in various tasks, including data visualization, image reconstruction, face recognition, and ZSL. By comparing with state-of-the-art representation learning methods, the outstanding results obtained validate the effectiveness of this method in the field of representation learning.

Intelligent medicine is eager to automatically generate radiology reports to ease the tedious work of radiologists. Previous researches mainly focused on the text generation with encoder-decoder structure, while CNN networks for visual features ignored the long-range dependencies correlated with textual information. Besides, few studies exploit cross-modal mappings to promote radiology report generation. To alleviate the above problems, we propose a novel end-to-end radiology report generation model dubbed Self-Supervised dual-Stream Network (S3-Net). Specifically, a Dual-Stream Visual Feature Extractor (DSVFE) composed of ResNet and SwinTransformer is proposed to capture more abundant and effective visual features, where the former focuses on local response and the latter explores long-range dependencies. Then, we introduced the Fusion Alignment Module (FAM) to fuse the dual-stream visual features and facilitate alignment between visual features and text features. Furthermore, the Self-Supervised Learning with Mask(SSLM) is introduced to further enhance the visual feature representation ability. Experimental results on two mainstream radiology reporting datasets (IU X-ray and MIMIC-CXR) show that our proposed approach outperforms previous models in terms of language generation metrics.

Recently some researches have focused on the Domain-Generalization (DG) Re-ID problem that training and testing are not in the same domain distribution. To fit the unseen complex scenes, recently deep feature matching-based methods for DG Re-ID have been developed and achieved the state-of-the-arts. However, they ignored some cases in which the accuracy of key region matching is unstable at a single scale, and the bad impact of style variations for feature representations. To address the issues, we propose a novel deep image matching model named Multi-scale Transformer-based Matching Network (MTMN) for DG Re-ID problem. MTMN matches two images with multi-scale local respondence instead of fixed representations. Specifically, the Transformer is carefully modified to formulate efficient local interactions between query and gallery images in multiple scales. Moreover, the style normalization is introduced to filter out identity-irrelated features to promote the matching results. Comprehensive experiments on several DG Re-ID tasks demonstrate the superiority of the proposed method compared with the state-of-the-arts, e.g., 5.4$\%$and 2.6$\%$gains in Rank-1 and mAP on Market-1501$\rightarrow$MSMT17(V1) task.

Collecting users’ historical data such as movie watching and music listening, and mining frequent items from them, can improve the utility of smart services, but there is also a risk of compromising user privacy. Local differential privacy is a strict definition of privacy and has been widely used in various privacy-preserving data collection scenarios. However, the accuracy of existing locally differentially private frequent items mining methods decreases significantly with the increase in the dimensions of data to be collected. In this paper, we propose a new locally differentially private frequent item mining method for high-dimensional data, which decreases the dimension used for data perturbation by grouping the contents and improving the interference matrix generation method, so as to improve the data reconstruction accuracy. The experimental results show that our proposed method can significantly improve the accuracy of frequent item mining and provide a better trade-off between privacy and accuracy compared with existing methods.

Many dimensionality reduction methods in the manifold learning field have the so-called small-sample-size (SSS) problem. Starting from solving the SSS problem, we first summarize the existing dimensionality reduction methods and construct a unified criterion function of these methods. Then, combining the unified criterion with the matrix function, we propose a general matrix function dimensionality reduction framework. This framework is configurable, that is, one can select suitable functions to construct such a matrix transformation framework, and then a series of new dimensionality reduction methods can be derived from this framework. In this article, we discuss how to choose suitable functions from two aspects: 1) solving the SSS problem and 2) improving pattern classification ability. As an extension, with the inverse hyperbolic tangent function and linear function, we propose a new matrix function dimensionality reduction framework. Compared with the existing methods to solve the SSS problem, these new methods can obtain better pattern classification ability and have less computational complexity. The experimental results on handwritten digit, letters databases, and two face databases show the superiority of the new methods.