本文選題：線性判別分析 + 判別準(zhǔn)則　； 參考：《浙江大學(xué)》2017年碩士論文

【摘要】：線性判別分析(Linear Discriminant Analysis,簡稱LD A)是特征提取的主要方法之一。LDA通過將高維模式樣本映射到具有最佳鑒別能力的低維空間,實(shí)現(xiàn)特征空間維數(shù)的壓縮和分類特征的提取,使映射后的模式樣本的類間距離最大和類內(nèi)距離最小,即模式在該空間中有最佳的可分離性。目前流行LDA算法存在小樣本、分離精度不高等不足,為了適應(yīng)廣泛的實(shí)際應(yīng)用要求,LDA算法優(yōu)化的研究成為研究熱點(diǎn)而意義深遠(yuǎn)。本文針對(duì)上述問題和研究背景,在前人的研究基礎(chǔ)上做了如下工作:1.闡述并總結(jié)了線性判別分析的基本理論。首先介紹了二分類問題下的LD A原理及推導(dǎo)過程,并推廣到多類問題;指出了 LDA中存在的相近類在最佳鑒別矢量上的投影不易區(qū)分的問題,總結(jié)了前人的解決方案并分析其優(yōu)缺點(diǎn),明確以解決該問題的改進(jìn)LDA算法為本文的研究點(diǎn)。2.從判別準(zhǔn)則優(yōu)化LD A。對(duì)于相近類在最佳鑒別矢量上的投影不易區(qū)分的問題,采用接近函數(shù)(Close)調(diào)節(jié)類間距離的權(quán)重,重新定義類間散度矩陣,改進(jìn)原有的Fisher準(zhǔn)則,使得類別均值之間相接近的類更好的分開,改善類間重疊或交叉的現(xiàn)象,從而提高了降維后各類樣本的區(qū)分度,更利于分類。3.仿真實(shí)驗(yàn)對(duì)算法性能比較分析。將文中改進(jìn)LDA算法進(jìn)行算法測試實(shí)驗(yàn)和ECG身份識(shí)別。實(shí)驗(yàn)結(jié)果表明,基于接近函數(shù)的改進(jìn)LDA算法能很好的解決相近類別不易區(qū)分的問題,且識(shí)別效果較好,算法性能良好。4.集成方法探討。指出了 LDA中存在的小樣本間題,分析并研究了克服該問題的最大散度差線性鑒別分析(MSLDA)算法,將文中改進(jìn)LDA算法和MSLDA算法簡單集成,并進(jìn)行ECG身份識(shí)別實(shí)驗(yàn)。集成的方法結(jié)合了二者的優(yōu)點(diǎn),為解決小樣本問題提供了思路,實(shí)驗(yàn)表明該方法的有效性。
[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.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP391.4

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