Multi-source remote sensing images can characterize the surface landscape from multiple dimensions including spectral,spatial,and topographic aspects,serving as a crucial data foundation for acquiring geospatial heterogeneity information,identifying land cover types,and supporting resource and environmental monitoring.Hyperspectral remote sensing image data and LiDAR data are frequently used jointly for image classification tasks.When jointly utilizing hyperspectral images and LiDAR data for classification,most existing studies em-ploy multi-scale feature extraction methods.However,the lack of interactive connections between feature infor-mation at different scales hinders the effectiveness of feature extraction and limits classification accuracy.Fur-thermore,differences between sensors in terms of observation mechanisms,spatial scales,and feature expression also pose challenges for the effective fusion of multi-source remote sensing data in geographical applications.To address these issues,a Multi-scale Cross-Interaction Encoding Network(MCIENet)is proposed.This network ef-fectively interacts feature information across scales and deeply fuses hyperspectral and LiDAR features to en-hance the classification performance of remote sensing images.Specifically,a Cross-scale Interaction Feature Ex-traction Module is first designed.It utilizes convolution kernels of different sizes to extract multi-scale features and connects features through up-sampling and down-sampling operations,enabling complementarity between features at different scales.To effectively fuse features from heterogeneous data sources,an Information-Perceiv-ing Fusion Encoding Module is designed.It employs a Gaussian-weighted guided Transformer encoder to learn inter-feature correlations,followed by a Cross-Branch Fusion Encoder to achieve deep fusion of multi-source re-mote sensing information.To validate the method's effectiveness,comparative experiments were conducted on four classic and widely used hyperspectral and LiDAR datasets.The results demonstrate that the proposed meth-od achieves superior classification performance compared to existing state-of-the-art methods.

Hyperspectral image (HSI) generally suffers from “homogeneity” and “heterogeneity” issues, leading to low intra-class consistency, poor inter-class differentiation, and higher misclassification rates in feature classification. Effectively integrating global structure and local details of spatial-spectral information is key to addressing this. Existing methods struggle to achieve this integration, which consequently impacts the classification performance. In this paper, we propose a hyperspectral remote sensing image classification method based on the domain-level complementarity of the spatial-spectral component (D2FuPro). This method utilizes a dual-branching structure to obtain information on the global overall structure and local details in the panoramic and mesoscopic domains, respectively. This dual-domain spatial-spectral complementarity aims to alleviate the above issues. A panoramic domain low-rank feature extraction method (PLFE) is designed in the first branch of the D2FuPro method. This method preserves the global spatial-spectral structure by low-rank modeling of the HSI. It combines texture smoothing to suppress noise and spectral anomalies and enhances intra-class spectral consistency. The second branch designs a method of mesoscopic domain feature enhancement (MDFE), which acquires the spectral information of features within the local range of HSI and utilizes the spatial structure of neighboring pixels to model, optimize the spatial boundaries, and enhance inter-class differentiation. Finally, fusing dual-domain information from both branches enables the realization of complementary spatial-spectral information in the panoramic and mesoscopic domains. A comparative experimental validation and analysis on four commonly used classical hyperspectral datasets demonstrates that the D2FuPro method outperforms traditional and twelve more advanced classification methods in terms of classification accuracy.

Hyperspectral images (HSIs) are gaining traction in consumer electronics for applications such as mobile health diagnostics, environmental monitoring, and agricultural quality assessment. However, effective practical deployment requires a rigorous balance between precise spectral-spatial feature extraction and computational efficiency. Existing hyperspectral image classification(HSIC) methods often fail to preserve oriented textures and edge details, limiting their usability in consumergrade systems. To address these challenges, we propose the Edge-Aware Fusion Network (EAF-Net), a multi-branch architecture that enhances edge preservation and robust spectral-spatial feature fusion. EAF-Net integrates: (1) An Oriented Feature Emphasis Spatial Branch that employs an Oriented Feature Emphasis Module to extract orientation-sensitive texture and boundary features. (2) A Multi-Scale Attention Spectral-Spatial Branch that groups spectral bands and applies spectral as well as multi-group spatial attention to emphasize informative bands and spatial contexts. (3) A Parallel Convolution Spectral Branch with compact 1×1 convolutions and non-linear convolution kernels to model cross-band interactions with low overhead. Experimental results on four public hyperspectral datasets show that, under the same training/testing protocol, EAF-Net outperforms selected baselines in terms of OA, AA, and Kappa, with notable gains in boundary pixel classification. The network, implemented with GPU acceleration, demonstrates strong performance and potential as a high-accuracy framework for hyperspectral image analysis.

In modern intelligent manufacturing, spindle thermal errors are critical to machining accuracy. To address this, we propose a two-stage prediction framework. First, for feature selection, an enhanced Red-Billed Magpie Optimization algorithm (RBMO-X) optimizes the parameters of a hybrid convolutional neural network (DLTK). Concurrently, PSO-optimized HDBSCAN clustering combined with Pearson correlation selects optimal temperature-sensitive points. The DLTK network integrates LSTM, deformable convolution, Transformer, and Fourier KAN modules for robust spatiotemporal feature extraction. The experimental results demonstrate significant improvements. The proposed feature selection method improves the Silhouette index by 32.39% and increases BWP by 49.16%. Using the selected points reduces prediction RMSE by 31.89% compared to random selection. The final RBMO-X-DLTK model achieves an RMSE of 0.181 mu m, an MAE of 0.128 mu m, and an R2 score of 0.9978, outperforming seven benchmark models (e.g., BP, LSTM, CNN-LSTM). In practical validation, the model enabled an average thermal error reduction of 89%. This integrated approach provides a robust and accurate solution for spindle thermal error prediction, demonstrating strong generalization capability.

In hyperspectral image classification (HSIC), each pixel contains information across hundreds of contiguous spectral bands; therefore, the ability to perform long-distance modeling that stably captures and propagates these long-distance dependencies is critical. A selective structured state space model (SSM) named Mamba has shown strong capabilities for capturing cross-band long-distance dependencies and exhibits advantages in long-distance modeling. However, the inherently high spectral dimensionality, information redundancy, and spatial heterogeneity of hyperspectral images (HSI) pose challenges for Mamba in fully extracting spatial–spectral features and in maintaining computational efficiency. To address these issues, we propose S2GL-MambaResNet, a lightweight HSI classification network that tightly couples Mamba with progressive residuals to enable richer global, local, and multi-scale spatial–spectral feature extraction, thereby mitigating the negative effects of high dimensionality, redundancy, and spatial heterogeneity on long-distance modeling. To avoid fragmentation of spatial–spectral information caused by serialization and to enhance local discriminability, we design a preprocessing method applied to the features before they are input to Mamba, termed the Spatial–Spectral Gated Attention Aggregator (SS-GAA). SS-GAA uses spatial–spectral adaptive gated fusion to preserve and strengthen the continuity of the central pixel’s neighborhood and its local spatial–spectral representation. To compensate for a single global sequence network’s tendency to overlook local structures, we introduce a novel Mamba variant called the Global_Local Spatial_Spectral Mamba Encoder (GLS2ME). GLS2ME comprises a pixel-level global branch and a non-overlapping sliding-window local branch for modeling long-distance dependencies and patch-level spatial–spectral relations, respectively, jointly improving generalization stability under limited sample regimes. To ensure that spatial details and boundary integrity are maintained while capturing spectral patterns at multiple scales, we propose a multi-scale Mamba encoding scheme, the Hierarchical Spectral Mamba Encoder (HSME). HSME first extracts spectral responses via multi-scale 1D spectral convolutions, then groups spectral bands and feeds these groups into Mamba encoders to capture spectral pattern information at different scales. Finally, we design a Progressive Residual Fusion Block (PRFB) that integrates 3D residual recalibration units with Efficient Channel Attention (ECA) to fuse multi-kernel outputs within a global context. This enables ordered fusion of local multi-scale features under a global semantic context, improving information utilization efficiency while keeping computational overhead under control. Comparative experiments on four publicly available HSI datasets demonstrate that S2GL-MambaResNet achieves superior classification accuracy compared with several state-of-the-art methods, with particularly pronounced advantages under few-shot and class-imbalanced conditions.

In the field of hyperspectral image classification, using spatial information as a supplement to spectral information has been widely applied. This article proposes a novel dual-scale complementary spatial-spectral joint classification model (DSCSM) to mitigate the issues of detail loss and insufficient utilization of spatial information, which traditionally lead to lower classification accuracy. In essence, the final classification result is obtained through decision fusion of two complementary feature extraction stages. In the preprocessing stage, a new dual-scale truncated filtering feature extraction method (DTFE) is proposed, which uses truncated filters with two different parameter settings to obtain two scales of smoothed patches, and then fuses them to obtain dual-scale structural features using Kernel principal component analysis. DTFE preserves edge information while smoothing details, effectively removing noise and retaining the dual-scale feature information. In the postprocessing stage, a sub-Markov random walk-based spatial probability optimization method is proposed, which models the spatial association of neighboring pixels, retaining complex textures as well as weak edge information to optimize the classification probability. Finally, the decision fusion strategy is employed to integrate the classification probabilities acquired from the aforementioned two stages. Comparative experiments on six different scene datasets with state-of-the-art classification methods validate that even with a small number of samples, DSCSM can achieve excellent object recognition performance. In addition, comprehensive parameter analysis proves the robustness and stability of the proposed method.

Graph neural networks (GNNs) have demonstrated significant potential in the field of computer vision in recent years, particularly in handling non-Euclidean data and capturing complex spatial and semantic relationships. This paper provides a comprehensive review of the latest research on GNNs in computer vision, with a focus on their applications in image processing, video analysis, and multimodal data fusion. First, we briefly introduce common GNN models, such as graph convolutional networks (GCN) and graph attention networks (GAT), and analyze their advantages in image and video data processing. Subsequently, this paper delves into the applications of GNNs in tasks such as object detection, image segmentation, and video action recognition, particularly in capturing inter-region dependencies and spatiotemporal dynamics. Finally, the paper discusses the applications of GNNs in multimodal data fusion tasks such as image–text matching and cross-modal retrieval, and highlights the main challenges faced by GNNs in computer vision, including computational complexity, dynamic graph modeling, heterogeneous graph processing, and interpretability issues. This paper provides a comprehensive understanding of the applications of GNNs in computer vision for both academia and industry and envisions future research directions.

Hyperspectral image (HSI) spectral-spatial joint feature (FE) extraction methods generally suffer from low feature retention and weak spatial-spectral dependence, which will lead to single-class feature confrontation (SCFC). To solve this problem, an unsupervised multivariate feature fusion network (M(3)FuNet) is developed in this article. In M(3)FuNet, multiscale supervector matrix correction (MSMC) and multiscale random convolution dispersion (MRCD) are used as the spectral and spatial feature extraction method, and the feature retention of spectral and spatial features is improved to achieve feature calibration by feature fusion and decision fusion, called "multivariate feature fusion." The MSMC is employed to correct the supervector matrix to reduce the intraclass variance in superpixel homogeneous regions and overcome the phenomenon of supervector block drift (SvBD). The MRCD uses random convolution and Gaussian smoothing to extract deep spatial features. Because of the similar feature representation ability of the MSMC and MRCD, the obtained spectral-spatial joint features have high feature retention and strong spectral-spatial dependence. Finally, this M(3)FuNet is used for realizing the classification of HSI. Three common HSI datasets are used to validate the effectiveness of the M(3)FuNet. The experiment results show that the M(3)FuNet has a superior performance compared with several state-of-the-art (SOTA) HSI classification methods. The code of the proposed M(3)FuNet is available at https://github.com/aichou233/M(3)FuNet.

Hyperspectral image (HSI) in Internet of Things (IoT) is a typical small sample data set, which is difficult and costly to label samples manually. In the feature extraction, it is difficult to increase the interclass distance and reduce the intraclass variance according to the limited label information, resulting in easy misclassification of the extracted features. To solve this problem, this article proposes an adaptive pseudo-label feature learning (APFL) model. In the APFL model, a hybrid distance pseudo-label generation (HDPG) method was designed to generate pseudo-labels by iterative multiscale superpixel segmentation using the spectral-spatial mixing distance information, while a pseudo-label feature generation (PFG) method was designed to generate pseudo-label features using pseudo-labels to capture the intraclass average vectors of HSI principal component features. Finally, the extracted pseudo-label features are classified at the pixel level. This APFL model can effectively reduce the intraclass variance and increase the interclass distance of the HSI data, thus improving the interclass separability. We have done comparative verification experiments on five commonly used HSI data sets in IoT. Compared with the current advanced feature extraction methods and classification methods, the proposed APFL model in this article has higher classification accuracy.

Discriminative marginalized least-squares regression (DMLSR) is unable to extract the spectral-spatial joint features, the proportion of learned interfering pixels is high. To solve this problem, a novel principal space approximation ensemble discriminant edge least-squares regression, namely PSAE-DMLSR is proposed for hyperspectral image classification. In the PSAE-DMLSR, a marginal principal component method (MP) is employed to search the optimal spectral subspace, and a principal space local marginal principal component (PSLMP) method is proposed to search the optimal representation space (ORS). In the PSLMP, a principal space representation (PSR) is designed to integrate the global spectral-spatial joint features information of the ORS, and the PSR is used to impose approximate averaging constraints and stochastic cascade fusion on the ORS, which can further improve the representation ability of the ORS. The ORS can effectively reduce the proportion of interfering pixels in DMLSR learning. It conducted comparative experiments with some more advanced classification methods on the three commonly used hyperspectral datasets. The experiment results show that the PSAE-DMLSR classification model can still obtain high classification accuracy under low hardware conditions, and the execution efficiency also has advantages.

Gate allocation is a combinatorial scheduling problem with multi-constraint and multi-objective. It is challenging to solve this problem when the size of flights increases continuously. As an adaptive technology with a random search ability, the genetic algorithm (GA) has been widely used for resource scheduling and combinatorial optimization. However, it is prone to slow convergence and falling into local optimal solutions. Therefore, an effective and robust GA based on hybrid multi-strategy of reverse learning, interval probability mutation, and phagocytosis mechanism, called RPIP-GA, is proposed to implement a new airport gate-allocation method. In the RPIP-GA, the population is divided into several subpopulations based on the fitness values of all individuals to prevent population degradation and improve population quality. The reverse learning strategy with elite retention is designed to initialize the population, expand the global search space, improve the quality of the original solution, and increase the population diversity. The phagocytosis mechanism is employed to implement a crossover operation to enhance the convergence rate and local search ability. An interval probability mutation technique is designed to improve the local search ability in the early stage and prevent falling into the local optimum in the later stage. The effectiveness of the RPIP-GA is validated using 45 complex functions selected from the benchmark functions and CEC 2017, 22 real-world engineering problems selected from CEC 2011, and an actual gate allocation problem via comparisons with the GA, PSO, GSA, DNLGSA, WMSDE, PADE, HIRCGA, and other algorithms. The experimental results show that the RPIP-GA can obtain optimal results with improved stability in most cases. The maximum allocation rate of actual airport gates reaches 98%, and the average convergence accuracy increases by 19% compared with that of the GA. The data used in the study is publicly available from the GitHub repository (https://github.com/xiaocangjiu).

With the development of sensor technology, the sources of remotely sensed image data for the same region are becoming increasingly diverse. Unlike single-source remote sensing image data, multisource remote sensing image data can provide complementary information for the same feature, promoting its recognition. The effective utilization of remote sensing image data from various sources can enhance the extraction of image features and improve the accuracy of feature recognition. Hyperspectral remote sensing (HSI) data and light detection and ranging (LiDAR) data can provide complementary information from different perspectives and are frequently combined in feature identification tasks. However, the process of joint use suffers from data redundancy, low classification accuracy and high time complexity. To address the aforementioned issues and improve feature recognition in classification tasks, this paper introduces a multiprobability decision fusion (PRDRMF) method for the combined classification of HSI and LiDAR data. First, the original HSI data and LiDAR data are downscaled via the principal component–relative total variation (PRTV) method to remove redundant information. In the multifeature extraction module, the local texture features and spatial features of the image are extracted to consider the local texture and spatial structure of the image data. This is achieved by utilizing the local binary pattern (LBP) and extended multiattribute profile (EMAP) for the two types of data after dimensionality reduction. The four extracted features are subsequently input into the corresponding kernel–extreme learning machine (KELM), which has a simple structure and good classification performance, to obtain four classification probability matrices (CPMs). Finally, the four CPMs are fused via a multiprobability decision fusion method to obtain the optimal classification results. Comparison experiments on four classical HSI and LiDAR datasets demonstrate that the method proposed in this paper achieves high classification performance while reducing the overall time complexity of the method.

As we take stock of the contemporary issue, remote sensing images are gradually advancing towards hyperspectral–high spatial resolution (H2) double-high images. However, high resolution produces serious spatial heterogeneity and spectral variability while improving image resolution, which increases the difficulty of feature recognition. So as to make the best of spectral and spatial features under an insufficient number of marking samples, we would like to achieve effective recognition and accurate classification of features in H2 images. In this paper, a cross-hop graph network for H2 image classification(H2-CHGN) is proposed. It is a two-branch network for deep feature extraction geared towards H2 images, consisting of a cross-hop graph attention network (CGAT) and a multiscale convolutional neural network (MCNN): the CGAT branch utilizes the superpixel information of H2 images to filter samples with high spatial relevance and designate them as the samples to be classified, then utilizes the cross-hop graph and attention mechanism to broaden the range of graph convolution to obtain more representative global features. As another branch, the MCNN uses dual convolutional kernels to extract features and fuse them at various scales while attaining pixel-level multi-scale local features by parallel cross connecting. Finally, the dual-channel attention mechanism is utilized for fusion to make image elements more prominent. This experiment on the classical dataset (Pavia University) and double-high (H2) datasets (WHU-Hi-LongKou and WHU-Hi-HongHu) shows that the H2-CHGN can be efficiently and competently used in H2 image classification. In detail, experimental results showcase superior performance, outpacing state-of-the-art methods by 0.75–2.16% in overall accuracy.

The high dimensionality of hyperspectral images (HSIs) brings significant redundancy to data processing. Band selection (BS) is one of the most commonly used dimensionality reduction (DR) techniques, which eliminates redundant information between bands while retaining a subset of bands with a high information content and low noise. The wild horse optimizer (WHO) is a novel metaheuristic algorithm widely used for its efficient search performance, yet it tends to become trapped in local optima during later iterations. To address these issues, an enhanced wild horse optimizer (IBSWHO) is proposed for HSI band selection in this paper. IBSWHO utilizes Sobol sequences to initialize the population, thereby increasing population diversity. It incorporates Cauchy mutation to perturb the population with a certain probability, enhancing the global search capability and avoiding local optima. Additionally, dynamic random search techniques are introduced to improve the algorithm search efficiency and expand the search space. The convergence of IBSWHO is verified on commonly used nonlinear test functions and compared with state-of-the-art optimization algorithms. Finally, experiments on three classic HSI datasets are conducted for HSI classification. The experimental results demonstrate that the band subset selected by IBSWHO achieves the best classification accuracy compared to conventional and state-of-the-art band selection methods, confirming the superiority of the proposed BS method.

Shared charging services have gained popularity for their contribution to green travel. Accurately identifying the core factors that influence user experience (UX) not only enhances service quality and optimizes user satisfaction, but also promotes the dissemination of green travel concepts. However, the influencing factors and their mechanisms vary significantly across regions, particularly along the Chengdu–Lhasa (G318) route, which features large elevation changes, diverse climatic conditions, rugged terrain, and frequent geological disasters, making the influencing factors particularly complex. This study analyzes comment texts from 38 shared charging stations along the G318 route in the e-Charging APP, totaling 15,214 comments. A comprehensive approach is employed, including high-frequency word analysis, term frequency–inverse document frequency (TF-IDF) comparison, co-occurrence semantic network and co-word matrix feature correlation analysis, Latent Dirichlet Allocation (LDA) topic modeling, and sentiment analysis. This multifaceted analysis explores core themes, user viewpoints, and sentiments in the comments, focusing on users’ perspectives on service quality, usage experience, and environmental impact of the charging stations. The findings indicate that charging speed, service attitude, environment, operational status of hardware and software, and pricing are key factors influencing user sentiment. Users have a high demand for the perfection of supporting facilities of shared charging stations, directly affecting user satisfaction and indirectly influencing the brand image and market competitiveness of enterprises.

Named entity recognition (NER) is an important task in Natural Language Processing (NLP), and Chinese NER is more difficult than English NER. Currently, machine learning and deep learning methods have been widely used in NER research. Traditional NER methods often ignore long-distance syntactic dependencies between words, and word preprocessing of such models usually ignores the contextual semantic information of the target word and fails to realize its polysemy. To address these shortcomings, this paper proposes a BERT-BiLSTM-GQA-CRF model for Chinese NER. BERT preprocessing language model generates word vectors representing contextual semantic information, inputs the sequence of trained word vectors into the BiLSTM layer embedded with Grouped-query attention (GQA) to obtain the overall semantic information, and finally decodes the sequence of entity tokens through the CRF layer. Compared to Multi-head attention (MHA), Multi-query attention (MQA) uses only a single key-value head, which can greatly speed up decoder inference. However, MQA leads to quality degradation, so in this paper, we use GQA to make the model more accurate than MHA with a speed comparable to MQA. Experimental results on the Weibo corpus and MSRA corpus show that the improved model improves both recognition effectiveness and speed.

The population structure of differential evolution (DE) algorithm cannot maintain the diversity of the population to the greatest extent and help the population avoid to fall into the local optima in time. In this paper, a co-evolutionary multi-swarm adaptive differential evolution algorithm, namely ECMADE is proposed to solve the premature convergence and search stagnation. First of all, in terms of population structure, based on the parallel distributed framework, ECMADE randomly and evenly divides the population into exploration subpopulation, development subpopulation, and auxiliary subpopulation, and introduces an adaptive information exchange mechanism so that subpopulations can escape local optima in time. Then, a multi-operator parallel search strategy is proposed to keep population diversity and meet the optimization needs of different problems. Finally, an adaptive adjustment mechanism of control parameters is developed, through recent elite parameter archive and weight distribution to fully mine successful parameter information, and generate control parameters with a high success rate for the current evolutionary stage. In order to prove the effectiveness of the ECMADE, 10 test functions and portfolio optimization problem are selected in here. The experiment results show that the ECMADE can effectively solve these test functions, the accuracy and efficiency is superior to those of two classical DE algorithms. The actual application results show that the ECMADE can significantly improve the ability of portfolio to resist extreme losses, which proves the effectiveness and feasibility of the ECMADE once again. The ECMADE has better optimization performance by comparing with some well-known algorithms in term of the solution quality, robustness and space distribution. It provides a new algorithm for solving complex optimization problems.

The flight operation data sharing not only brings huge benefits to all participants, but also puts forward higher requirements for data security. Consortium blockchain provides a new approach to safely sharing flight operation data in an untrusted environment. Practical Byzantine Fault-Tolerant (PBFT) algorithm is one of the most widely used consensus algo-rithms in consortium blockchain, but it exists some problems, such as static structure, low consensus efficiency and large communication overhead. To solve these problems, a PBFT with grouping score mechanism and artificial bee colony-optimized consensus process, namely ABC-GSPBFT, is designed to construct the consortium blockchain for sharing flight operation data. Firstly, the artificial bee colony algorithm is used to pre-select a collection of reliable nodes to narrow the scope of consensus. Then, the grouping score mechanism is employed to dynamically update the consensus nodes to further narrow the scope of con-sensus and enhance the reliability of consensus nodes. Finally, the commit stage of the PBFT algorithm is reasonably simplified to improve consensus efficiency. The actual flight operation data is selected to test and verify the effectiveness of the ABC-GSPBFT algorithm. The analysis and experimental results show that the ABC-GSPBFT algorithm can greatly reduce consensus delay and communication overhead, and improve dynamic performance and consensus efficiency of the flight data sharing. It is an effective method for safely, reli-ably and efficiently sharing flight data.(c) 2022 Elsevier Inc. All rights reserved.

This paper proposes a spectral clustering method using k-means and weighted Mahalanobis distance (Referred to as MDLSC) to enhance the degree of correlation between data points and improve the clustering accuracy of Laplacian matrix eigenvectors. First, we used the correlation coefficient as the weight of the Mahalanobis distance to calculate the weighted Mahalanobis distance between any two data points and constructed the weighted Mahalanobis distance matrix of the data set; then, based on the weighted Mahalanobis distance matrix, we used the K-nearest neighborhood (KNN) algorithm construct similarity matrix. Secondly, the regularized Laplacian matrix was calculated according to the similarity matrix, normalized and decomposed, and the feature space for clustering was obtained. This method fully considered the degree of linear correlation between data and special spatial structure and achieved accurate clustering. Finally, various spectral clustering algorithms were used to conduct multi-angle comparative experiments on artificial and UCI data sets. The experimental results show that MDLSC has certain advantages in each clustering index and the clustering quality is better. The distribution results of the eigenvectors also show that the similarity matrix calculated by MDLSC is more reasonable, and the calculation of the eigenvectors of the Laplacian matrix maximizes the retention of the distribution characteristics of the original data, thereby improving the accuracy of the clustering algorithm.

In order to further improve the effectiveness of homomorphic cryptography, we optimize Lauter et al. 's partial homomorphic cryptography scheme, and propose a new RLWE-based total homomorphic cryptography (FHE) scheme, which combines a series of existing techniques with the Chinese residual theory, and merges several “plaintext slots” into a ciphertext for homomorphic computation. The extended key transformation technology and modulo transformation technology are used to reduce the noise of ciphertext and enable it to carry out the next homomorphic operation. Compared with the original scheme, the security and effectiveness of the scheme were studied on the premise of ensuring CPA security, and the results showed that the performance of the scheme was improved by N times.