判别准则优化的LDA研究

发布时间：2018-07-11 17:39

本文选题：线性判别分析 + 判别准则　；参考：《浙江大学》2017年硕士论文

【摘要】：线性判别分析(Linear Discriminant Analysis,简称LD A)是特征提取的主要方法之一。LDA通过将高维模式样本映射到具有最佳鉴别能力的低维空间,实现特征空间维数的压缩和分类特征的提取,使映射后的模式样本的类间距离最大和类内距离最小,即模式在该空间中有最佳的可分离性。目前流行LDA算法存在小样本、分离精度不高等不足,为了适应广泛的实际应用要求,LDA算法优化的研究成为研究热点而意义深远。本文针对上述问题和研究背景,在前人的研究基础上做了如下工作:1.阐述并总结了线性判别分析的基本理论。首先介绍了二分类问题下的LD A原理及推导过程,并推广到多类问题;指出了 LDA中存在的相近类在最佳鉴别矢量上的投影不易区分的问题,总结了前人的解决方案并分析其优缺点,明确以解决该问题的改进LDA算法为本文的研究点。2.从判别准则优化LD A。对于相近类在最佳鉴别矢量上的投影不易区分的问题,采用接近函数(Close)调节类间距离的权重,重新定义类间散度矩阵,改进原有的Fisher准则,使得类别均值之间相接近的类更好的分开,改善类间重叠或交叉的现象,从而提高了降维后各类样本的区分度,更利于分类。3.仿真实验对算法性能比较分析。将文中改进LDA算法进行算法测试实验和ECG身份识别。实验结果表明,基于接近函数的改进LDA算法能很好的解决相近类别不易区分的问题,且识别效果较好,算法性能良好。4.集成方法探讨。指出了 LDA中存在的小样本间题,分析并研究了克服该问题的最大散度差线性鉴别分析(MSLDA)算法,将文中改进LDA算法和MSLDA算法简单集成,并进行ECG身份识别实验。集成的方法结合了二者的优点,为解决小样本问题提供了思路,实验表明该方法的有效性。
[Abstract]:Linear discriminant Analysis (LD A) is one of the main methods of feature extraction. LDA can compress the dimension of feature space and extract classification features by mapping high-dimensional pattern samples to low-dimensional space with the best discriminant ability. The best separability of the schema in this space is to maximize the distance between classes and to minimize the intra-class distance of the mapped schema samples. At present, the popular LDA algorithm has some shortcomings, such as small sample and low separation precision. In order to meet the needs of extensive practical application, the research of LDA algorithm optimization has become a hot topic and has far-reaching significance. In this paper, in view of the above problems and research background, on the basis of previous studies, we do the following work: 1. The basic theory of linear discriminant analysis is expounded and summarized. Firstly, the principle and derivation of LD A for two classification problems are introduced and extended to many kinds of problems, and the problem that the projection of similar classes in LDA is difficult to distinguish on the best discriminant vector is pointed out. This paper summarizes the previous solutions and analyzes their advantages and disadvantages, and makes it clear that the improved LDA algorithm to solve this problem is the research point of this paper. LD A. For the problem that the projection of similar classes on the best discriminant vector is difficult to distinguish, close function is used to adjust the weight of the distance between classes, the dispersion matrix between classes is redefined, and the Fisher criterion is improved. It makes the classes with similar mean values better separated, and improves the overlap or crossover between classes, thus increasing the classification of all kinds of samples after dimensionality reduction, which is more conducive to classification. 3. The performance of the algorithm is compared and analyzed by simulation experiments. The improved LDA algorithm is used for algorithm testing and ECG identification. The experimental results show that the improved LDA algorithm based on proximity function can solve the problem that the similar classes are difficult to distinguish, and the recognition effect is good, and the performance of the algorithm is good. 4. Discussion on the method of integration. This paper points out the problems among small samples in LDA, analyzes and studies the maximum divergence linear discriminant analysis (MSLDA) algorithm to overcome this problem, integrates the improved LDA algorithm and MSLDA algorithm, and carries out ECG identification experiments. The integrated method combines the advantages of the two methods and provides a way to solve the problem of small samples. The experimental results show that the method is effective.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.4

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