基于自适应加权的多类线性判别分析降维算法研究

发布时间：2018-02-24 10:41

本文关键词： 降维算法 Fisher准则线性判别分析多类问题自适应加权　出处：《安徽大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着信息技术的发展,越来越多的应用会采集并使用大量的高维数据来解决某些问题。数据的维度越高,所包含的信息量就越大,会方便我们使用和挖掘数据信息。但与此同时,高维的特征空间会给数据处理带来诸多不便,例如计算复杂、存储量增加等等,甚至会因为信息冗余使实验结果不理想。应对此"维度灾难"带来的诸多问题,降维算法变得尤为重要。降维算法是一种将高维数据降为低维数据的方法,通过该方法得到的数据在低维空间中既保留了主要的特征信息,又去除了冗余信息,提高了数据有效性,是一种非常经典的机器学习方法。传统的数据降维算法有线性判别分析(LDA)和主成分分析(PCA)等,这些经典方法自提出以来被不断地研究,发现其缺陷和不足,提出新的改进思路,使降维技术更加精湛有效。本文主要针对LDA算法的缺陷,对于多类降维问题做了相应的研究与改进。LDA算法的目标函数过于依赖大距离的类间距,使得小距离的类间距会被忽略,导致投影空间的类与类之间重叠增加。本文的算法主要解决此类问题。本文的主要贡献点有:(1)本文提出一种基于柯西不等式的自适应加权多类线性判别分析算法,该算法在传统的线性判别分析算法的基础上采用类对的距离计量方式,并用自适应加权的方法解决LDA在多类问题中的重叠问题。(2)本文提出一种基于概率矩阵的自适应加权多类线性判别分析方法,该方法对每个类对分别计算类间散度矩阵和类内散度矩阵,并对每个类对的概率参数进行加权,通过自适应加权使得投影空间中的类间距尽可能相等。相比于基于柯西不等式的自适应加权多类线性判别分析算法,该方法增加了正则化项作为惩罚项,通过参数调节使模型更优。
[Abstract]:With the development of information technology, more and more applications will collect and use a lot of high-dimensional data to solve some problems. It makes it easier for us to use and mine data information, but at the same time, high-dimensional feature spaces can cause a lot of inconvenience to data processing, such as computational complexity, increased storage, and so on. Even because of the redundancy of information, the experimental results are not ideal. The dimensionality reduction algorithm is a method to reduce the high-dimensional data to low-dimensional data, which is especially important for the problems caused by the "dimensionality disaster". The data obtained by this method not only retain the main feature information in the low dimensional space, but also eliminate the redundant information, and improve the data validity. Traditional data dimensionality reduction algorithms include linear discriminant analysis (LDA) and principal component analysis (PCAA). These classical methods have been continuously studied since they were put forward. Aiming at the defects of LDA algorithm, this paper studies and improves the multiclass dimensionality reduction problem. The objective function of .LDA algorithm is too dependent on the class spacing of long distance, so that the small distance between classes will be ignored. The algorithm of this paper mainly solves this kind of problem. The main contribution of this paper is: (1) this paper proposes an adaptive weighted multiclass linear discriminant analysis algorithm based on Cauchy inequality. Based on the traditional linear discriminant analysis (LDA) algorithm, this algorithm adopts the distance metering method of class pairs. In this paper, an adaptive weighted multiclass linear discriminant analysis method based on probability matrix is proposed to solve the overlapping problem of LDA in multi-class problems. In this method, the inter-class divergence matrix and intra-class divergence matrix are calculated for each class pair, and the probability parameters of each class pair are weighted. Compared with the adaptive weighted multiclass discriminant analysis algorithm based on Cauchy inequality, the regularization term is added as the penalty term. The model is optimized by adjusting the parameters.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP181

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