多步扩散映射得到样本紧凑分布的降维方法  

Dimensionality Reduction Method for Compact Sample Distribution Using Multi-Step Diffusion Mapping

作　　者：贺忠海 贾琼 冯占波 张晓芳[3] He Zhonghai;Jia Qiong;Feng Zhanbo;Zhang Xiaofang(School of Control Engineering,Northeastern University at Qinhuangdao,Qinhuangdao 066004,Hebei,China;Hebei Key Laboratory of MicroNano Sensing,Qinhuangdao 066004,Hebei,China;School of Optics and Photonics,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]东北大学秦皇岛分校控制工程学院,河北秦皇岛066004 [2]河北省微纳精密光学传感与检测技术重点实验室,河北秦皇岛066004 [3]北京理工大学光电学院,北京100081

出　　处：《光学学报》2024年第20期285-293,共9页Acta Optica Sinica

基　　金：河北省自然科学基金(F2020501040)。

摘　　要：将高维光谱数据降维至二维并绘制散点图,可以直观地观察点云分布情况,从而判断模型更新时机。目前的降维方法得到的样本分布过于分散,分散的点云分布会覆盖新样本的点,从而使样本的新颖性难以判断。进行多步扩散可以实现样本点在平面的紧凑显示,因此提出多步扩散映射的降维方法。基于数据集自身性质,给出自动确认最适合的带宽值以及扩散步数的方法。针对高斯核函数的核带宽,使用线性最优位置确定带宽值,而针对扩散步数,则通过寻找熵值曲线的拐点位置来确定最优步数。相比于传统的主成分分析(PCA)降维方法,多步扩散映射方法得到的二维散点图中样本点的分布更加紧凑,具有差异性的新样本在图中更加容易判断。Objective Spectroscopy detection is widely used in industrial process measurement due to its speed,noncontact nature,and capability for multicomponent measurement.However,spectral measurements need to be analyzed using a stoichiometric model to obtain concentration values.Environmental changes during model establishment and use can affect the accuracy of predictions for new data,which necessitates periodic model updates.Therefore,it is important to study the timing of spectral model updates.By reducing highdimensional spectral data to two dimensions and creating scatter plots,one can visually observe the point cloud distribution and judge when to update the model.The current dimensionality reduction methods result in a scattered sample distribution,where the scattered point cloud can obscure new sample points,making it difficult to assess the novelty of new samples.We find that the multistep diffusion process enables a more compact representation of sample points in the plane,which facilitates better judgment of when the model should be updated.Consequently,we propose a dimensionality reduction method based on multistep diffusion mapping.Methods Our research method is based on the fundamental principle of diffusion mapping.Firstly,the Gaussian kernel function is used to calculate the similarity matrix K of the sample points.Subsequently,the obtained similarity matrix K is normalized to derive the Markov probability transition matrix.Next,multistep diffusion is performed on the onestep probability transition matrix to obtain the multistep diffusion probability matrix.This matrix is then transformed into diffusion distances,and the lowdimensional coordinates of the dataset are computed using classical multidimensional scaling(CMDS).To select the bandwidth value of the kernel function,we construct the similarity matrix W related to the kernel bandwidth based on the Euclidean distance between the sample points.Summing all elements in the similarity matrix yields a function related to the kernel bandwidth.Initially,we

关 键 词：光谱学 模型更新 多步扩散 紧凑显示 核宽度确定 最优扩散步数 

分 类 号：O433.1[机械工程—光学工程]