基于扩散映射的太赫兹光谱识别

特征提取对于太赫兹光谱识别来说至关重要。传统方法是通过人工选取太赫兹光谱中差异性较大的吸收峰作为特征进行光谱识别，但当部分物质在太赫兹波段没有明显波峰、波谷等光谱图形特征时，这种方式便不再适用。为此，研究人员利用统计学习与机器学习方法对高维太赫兹光谱数据进行降维和特征提取。由于物质的太赫兹光谱数据各维度呈现非线性，尤其是当不同物质的太赫兹光谱曲线整体非常相似时，线性处理方法易产生较大误差。针对这一问题，提出了一种基于扩散映射(DM)的太赫兹光谱识别方法。扩散映射能在保持数据内在几何结构的同时对其进行非线性降维，提取的流形特征区分度较高，对数据还有聚类效果。首先用S-G滤波器对Alloxazine等10种物质的太赫兹光谱样本进行滤波，并用三次样条插值法对截取相同频段后的光谱样本进行统一分辨率处理；然后利用DM将高维太赫兹光谱数据映射到低维特征空间并提取太赫兹光谱的流形特征；最后用多分类支持向量机(M-SVM)对十种物质的太赫兹透射光谱进行分类。实验结果表明，相比于主成分分析(PCA)和等距映射(ISOMAP)，使用DM提取的太赫兹光谱流形特征具有更高的区分度，而且DM可以直接得到太赫兹光谱数据本征维数的估计值，这为相似太赫兹光谱的快速精准识别提供了一条新的途径。

Terahertz Spectroscopic Identification with Diffusion Maps

Feature extraction is the key issue for the identification of terahertz spectroscopy.For the traditional method,it is identified by different absorption peaks as the features that extracted through manual method.However,for many materials,there are no apparent spectral graphics features in the terahertz band,such as peaks,valleys and etc.To this end,the researchers reduce the dimension from the high-dimensional terahertz spectroscopy data and extract the features through statistics learning and machine learning methods.Linear method is easy to cause greater error due to the nonlinear nature of terahertz spectroscopy data,especially when different materials of spectrum curves are very similar.To address this issue,a novel terahertz spectroscopy identification approach with Diffusion Maps(DM)was studied in this paper.Diffusion Maps can realize nonlinear dimensionality reduction while maintaining the internal geometry of the data.In addition,the manifold features extracted by the method have good discrimination and clustering performance.Firstly,S-G filter and cubic spline interpolation were used to smooth and uniform the resolution of terahertz transmission spectra of ten kinds of substances in the same frequency band.Secondly,high-dimensional data of terahertz spectra is mapped to the low-dimensional feature space by using DM so that we can extract the manifold features of terahertz spectroscopy.Finally,a Multi-class Support Vector Machine(M-SVM)classifier is applied to classify these terahertz spectra.Experimental results show that,compared with Principal Component Analysis(PCA)and Isometric Mapping(ISOMAP),manifold features of terahertz spectroscopy extracted by DM have higher degree of differentiation.Besides,DM can get the estimation of intrinsic dimension of terahertz spectra directly.So this proposed method provides a novel approach to identify similar terahertz spectrum quickly and accurately.