自适应近邻局部比值和线性判别分析算法

doi:10.3778/j.issn.1002-8331.2204-0348

摘要/Abstract

摘要： 在机器学习和模式识别中，降维能够显著提升分类器的判别性能与效率。比率和（ratio sum，RS）是线性判别分析（linear discriminant analysis，LDA）的一种全新变体，它试图使投影矩阵在每个维度上都达到最优。但RS并没有考虑到数据的局部几何结构，这就可能导致无法求得最优解。为了克服RS的这一缺点，提出了一种自适应近邻局部比值和线性判别分析算法（adaptive neighbor local ratio sum linear discriminant analysis，ANLRSLDA）。该算法使用自适应近邻的构图方法构建邻接矩阵，保留数据的局部几何结构完成了数据类间及类内矩阵的构建，从而更好地找到数据的最优表示；并且该方法采用有效的无核参数邻域分配策略来构造邻接矩阵，避免调整热核参数的需要。在UCI数据集及人脸数据集进行了对比实验，验证了该算法的有效性。

关键词: 降维, 比值和, 线性判别分析, 自适应近邻

Abstract: In machine learning and pattern recognition, dimension reduction can significantly improve the discriminative performance and efficiency of the classifier. Ratio sum（RS）is a completely new variant of linear discriminant analysis（LDA） that tries to optimize the projection matrix in every dimension. However, the RS does not take into account the local geometry of the data, which may lead to the failure to obtain the optimal solution. To overcome this disadvantage of RS, an adaptive neighbor local ratio sum linear discriminant analysis algorithm is proposed. The algorithm uses the adaptive neighbor composition method to construct the neighbor matrix, retains the local geometric structure of the data to complete the construction between and within the data matrix, so as to better find the optimal representation of the data. And the method adopts the effective kernel-free parameter neighborhood allocation strategy to construct the neighbor matrix, to avoid the need to adjust the heat core parameters. Finally, comparative experiments on the UCI dataset verifies the effectiveness of the algorithm.

Key words: dimensionality reduction, ratio sum（RS）, linear discriminant analysis（LDA）, adaption neighbor comparative

张家乐, 林浩申, 周科艺, 孙博, 杨晓君. 自适应近邻局部比值和线性判别分析算法[J]. 计算机工程与应用, 2023, 59(15): 115-122.

ZHANG Jiale, LIN Haoshen, ZHOU Keyi, SUN Bo, YANG Xiaojun. Adaptive Neighbor Local Ratio Sum Linear Discriminant Analysis[J]. Computer Engineering and Applications, 2023, 59(15): 115-122.

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