基于线性回归的多维数据半监督维数约减方法探究  

Exploration of Semi Supervised Dimensionality Reduction Method for Multidimensional Data Based on Linear Regression

作　　者：林敏 龚让声[2] LIN Min;GONG Rang-sheng(School of Computer Information,Minnan Science and Technology College,Quanzhou 362000,China;Xiamen Huatian International Vocation College,Xiamen 361102,China)

机构地区：[1]闽南科技学院计算机信息学院,福建泉州362000 [2]厦门华天涉外职业技术学院,福建厦门361102

出　　处：《遵义师范学院学报》2025年第1期88-91,96,共5页Journal of Zunyi Normal University

基　　金：福建省教育厅中青年教师科研项目(JAT160675,JAT191046)。

摘　　要：多维数据约减时,并未考虑数据本身的结构,无法较好地保留原始数据结构,影响数据维数约减效果,为此,研究基于线性回归的多维数据半监督维数约减方法。利用正交增量子空间类标传播算法,将有类标多维数据样本标记无类标多维数据样本通过线性回归,建立样本稀疏表示正则项;结合稀疏表示正则项,设计半监督维数约减目标函数,获取最大广义特征值相应的特征向量,构建多维数据的投影矩阵,将多维数据投影成低维数据,完成半监督维数约简。实验结果表明,在不同多维数据维数时,该方法约减维数的最低轮廓系数在0.839左右,轮廓系数较高,不同网络攻击时,安全性较高。When reducing multidimensional data,the structure of the data itself is not considered,which makes it difficult to preserve the original data structure and affects the dimensionality reduction effect.Therefore,a semi supervised dimensionality reduction method for multidimensional data based on linear regression is studied.Using the orthogonal incremental subspace class label propagation algorithm,label multi-dimensional data samples with class labels with multi-dimensional data samples without class labels,establishing a sample sparse representation regularization term through linear regression,combining sparse representation regularization terms,designing a semi supervised dimensionality reduction objective function to obtain the eigenvectors corresponding to the maximumgeneralized eigenvalues,constructing a projection matrix for multidimensional data,projecting multidimensional data into low dimensional data,and completing semi-supervised dimensionality reduction.The experimental results show that at different dimensions of multidimensional data,the minimumsilhouette coefficient of this method for dimensionality reduction is around 0.839,which is relatively high.It has high security under different network attacks.

关 键 词：增量子空间 多维数据 半监督 维数约减 线性回归 目标函数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]