多维数据判别分析的非参核密度算法研究
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摘要
判别分析在数据挖掘、识别中有着广泛的应用,其中充分利用训练集的信息,改进判别规则算法,降低误判率一直是众多研究关注的焦点。传统的一些判别算法中,往往事先假定数据的分布类型来建立判别规则,但多维数据结构往往存在违背假定的情形,从而导致较高的误判率。针对此类问题,提出采用非参核密度算法建立多维数据的判别规则,同时通过Iris数据和Seeds数据进行实证分析。结果表明,与现有的判别分析算法相比较,所提判别算法利用样本资料信息更充分,显著提高了多维数据的判别精度,并且该算法不受分布假定的限制,具有广泛的适用性。
Discriminant analysis is widely used in data mining and recognition. How to make full use of the information of training sets, and how to improve the algorithm of discriminant rules and reduce the rate of misjudgement has always been the focus for many researches. In some traditional algorithms, the distribution type of data is often assumed firstly,but the structures of multidimensional data often violate the assumptions and lead to a higher rate of misjudgment. Aiming at such problems, this paper proposes to establish discriminant rules by the algorithm of nonparametric kernel density, and carries out empirical analysis through Iris and Seeds data. The results show that compared with the existing discriminant analysis algorithms, the proposed algorithm uses the information of data more fully, and significantly improves the accuracy of the multidimensional data. At the same time, this algorithm is not restricted by the distribution assumption, so it has wide applicability.
Discriminant analysis is widely used in data mining and recognition. How to make full use of the information of training sets, and how to improve the algorithm of discriminant rules and reduce the rate of misjudgement has always been the focus for many researches. In some traditional algorithms, the distribution type of data is often assumed firstly,but the structures of multidimensional data often violate the assumptions and lead to a higher rate of misjudgment. Aiming at such problems, this paper proposes to establish discriminant rules by the algorithm of nonparametric kernel density, and carries out empirical analysis through Iris and Seeds data. The results show that compared with the existing discriminant analysis algorithms, the proposed algorithm uses the information of data more fully, and significantly improves the accuracy of the multidimensional data. At the same time, this algorithm is not restricted by the distribution assumption, so it has wide applicability.
引文
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[16]Rao P.Nonparametric functional estimation[J].Journal of the American Statistical Association,1983,81(393):483-512.
[2]李佐静,李清,凌俊红,等.Bayes判别分析在基于儿茶酚胺的阿尔茨海默病预测研究中的应用[J].计算机与应用化学,2013,24(8):447-450.
[3]任冬梅,张宇洋,董新玲.应用于石油钻井安全评价的改进主成分分析-贝叶斯判别方法[J].计算机应用,2017,37(6):1820-1824.
[4]杨可明,刘二维,卓伟,等.谐波能量谱特征向量的高光谱影像Bayes分类[J].计算机应用研究,2017,34(5):1585-1589.
[5]Yao C,Cheng G.Approximative Bayes optimality linear discriminant analysis for Chinese handwriting character recognition[J].Neurocomputiong,2016,207:346-353.
[6]李定坤,陈建华,林智健.一种基于统计学和凸二次规划的模式识别方法[J].模式识别与人工智能,1996,9(4):311-316.
[7]彭红毅,蒋春福,朱思铭.基于ICA与Bayes的判别分析模型[J].计算机应用研究,2007,24(8):58-59.
[8]路梅,李凡长.领域嵌入的张量学习[J].计算科学与探索,2017,11(7):1102-1113.
[9]余景丽,胡恩良,张涛.一种新的L1度量Fishe线性判别分析研究[J].计算机工程与应用,2018,54(4):128-134.
[10]彭小智,吴和成.基于非参数方法的Bayes判别分析[J].统计与决策,2015(22):68-70.
[11]艾天霞,张蕾.传统Bayes判别与非参数核密度Bayes判别的比较[J].江南大学学报(自然科学版),2015,14(5):677-680.
[12]Rosenblatt M.Remarks on some nonparametric estimates of a density function[J].The Annals of Mathematical Statistics,1956,27(3):832-837.
[13]Parzen E.On estimation of a probability denstity function and mode[J].The Annals of Mathematical Statistics,1962,1065-1067.
[14]Silverman B W.Density estimation for statistics and data analysis[M].London:Chapman&Hall,1986:296-297.
[15]孙志华,尹俊平,陈菲菲,等.非参数与半参数统计[M].北京:清华大学出版社,2016:9-33.
[16]Rao P.Nonparametric functional estimation[J].Journal of the American Statistical Association,1983,81(393):483-512.