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With the rapid advancements in data analysis and the increasing complexity of high-dimensional datasets, traditional dimensionality reduction techniques like Local Linear Embedding (LLE) often face challenges in maintaining accuracy and efficiency. This research aims to overcome the limitations of LLE, specifically its reliance on the nearest neighbor concept, its inability to distinguish differences among manifold points, and its underutilization of data discrimination information. To address these issues, we propose an advanced LLE algorithm that integrates decision tree-based neighbor recognition with Gaussian kernel density estimation. Decision trees accurately determine neighboring relationships, which are then optimized using Gaussian kernel density estimation to better reflect the distribution of sample points on the manifold. The algorithm also incorporates data discrimination information to enhance classification accuracy and efficiency. Evaluations in facial recognition tasks using SVM classifiers demonstrate significant improvements. Integrating decision trees (LLE-DT) yielded accuracy gains, with LFW at 98.75%, CFP 96.10%, and Olivetti 92.18%. Gaussian density estimation (LLE-GDE) achieved further enhancements, especially in LFW (99.13%), with CFP at 96.85%, and Olivetti at 91.82%. Combining both methods (LLE-DT-GDE) led to substantial improvements: LFW 99.61%, CFP 97.23%, and Olivetti 93.56%, highlighting the synergy between decision trees and Gaussian estimation. This advanced LLE algorithm effectively addresses the limitations of traditional approaches, showing promising results in complex data processing tasks such as facial recognition. These findings suggest its potential for broader applications in fields requiring robust data analysis and classification. [ABSTRACT FROM AUTHOR]

This study addresses the challenges of setting segmentation points in the membership function and determining appropriate weights for different types of information within a fuzzy logic algorithm for map matching. We use linear fitting to derive an empirical formula for setting segmentation points for the information membership function. Furthermore, we evaluate the effects of various weights for direction and distance information in parallel and cross-road scenarios. The research identified the optimal distance that achieves the highest matching accuracy and provided insights into how the weights of connection, direction, and distance information affect this accuracy. The simulations confirmed the critical importance of precise segmentation point settings and weight determinations in enhancing the accuracy of fuzzy logic algorithms for map matching. The results underscore the potency of our tailored parameter-setting strategy and contribute to knowledge of symmetry, offering practical insights for implementing fuzzy logic in map matching with a particular emphasis on the principle of symmetry in algorithm design and information processing. [ABSTRACT FROM AUTHOR]

Infrared image recognition technology can work day and night and has a long detection distance. However, the infrared objects have less prior information and external factors in the real-world environment easily interfere with them. Therefore, infrared object classification is a very challenging research area. Manifold learning can be used to improve the classification accuracy of infrared images in the manifold space. In this article, we propose a novel manifold learning algorithm for infrared object detection and classification. First, a manifold space is constructed with each pixel of the infrared object image as a dimension. Infrared images are represented as data points in this constructed manifold space. Next, we simulate the probability distribution information of infrared data points with the Gaussian distribution in the manifold space. Then, based on the Gaussian distribution information in the manifold space, the distribution characteristics of the data points of the infrared image in the low-dimensional space are derived. The proposed algorithm uses the Kullback-Leibler (KL) divergence to minimize the loss function between two symmetrical distributions, and finally completes the classification in the low-dimensional manifold space. The efficiency of the algorithm is validated on two public infrared image data sets. The experiments show that the proposed method has a 97.46% classification accuracy and competitive speed in regards to the analyzed data sets. [ABSTRACT FROM AUTHOR]