基于随机游走扩散映射的降维算法  

DIMENSION REDUCTION ALGORITHM BASED ON RANDOM WALK DIFFUSION MAPPING

作　　者：薛艳锋 王三虎[3] 高志娥[3] 高永强[3] Xue Yanfeng;Wang Sanhu;Gao Zhie;Gao Yongqiang(School of Computer and Information Technology,Shanxi University,Taiyuan 030006,Shanxi,China;Institute of Complex Systems,Shanxi University,Taiyuan 030006,Shanxi,China;Department of Computer Science and Technology,Luliang University,Lvliang 033000,Shanxi,China)

机构地区：[1]山西大学计算机与信息技术学院,山西太原030006 [2]山西大学复杂系统研究所,山西太原030006 [3]吕梁学院计算机科学与技术系,山西吕梁033000

出　　处：《计算机应用与软件》2022年第3期266-269,共4页Computer Applications and Software

基　　金：山西省高等学校科技创新项目(2020L0715);山西省教育厅教学改革项目(J2018195)。

摘　　要：传统数据降维算法分为线性或流形学习降维算法,但在实际应用中很难确定需要哪一类算法。设计一种综合的数据降维算法,以保证它的线性降维效果下限为主成分分析方法且在流形学习降维方面能揭示流形的数据结构。通过对高维数据构造马尔可夫转移矩阵,使越相似的节点转移概率越大,从而发现高维数据降维到低维流形的映射关系。实验结果表明,在人造数据以及真实数据的线性降维中,该算法降维效果与主成分分析算法相当而局部线性嵌入失败;在流形学习降维中,该算法与局部线性嵌入基本相当而主成分分析算法完全失败。Traditional data dimensionality reduction algorithms are divided into linear or manifold learning dimensionality reduction algorithms,but in practical applications,it is difficult to determine which kind of algorithm is needed.A comprehensive data dimensionality reduction algorithm is designed to ensure that the lower limit of its linear dimensionality reduction effect is the principal component analysis(PCA)algorithm,and the data structure of manifold can be revealed in the aspect of manifold learning dimensionality reduction.By constructing Markov transition matrix for high-dimensional data,the more similar nodes have greater transition probability,so as to find the mapping relationship between high-dimensional data dimensionality reduction and low-dimensional manifold.The experimental results show that in the linear dimensionality reduction of artificial data and real data,the dimensionality reduction effect of this algorithm is equivalent to that of PCA algorithm,while the locally linear embedding(LLE)failed.In the manifold learning dimensionality reduction,this algorithm is basically equivalent to that of LLE,but PCA algorithm fails completely.

关 键 词：降维 主成分分析 局部线性嵌入 扩散映射 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]