一种改进的主成分分析特征抽取算法:YJ-MICPCA

针对主成分分析(PCA)假设数据服从高斯分布的条件以及只能处理特征之间线性关系的不足,提出一种基于Yeo-Johnson变换和最大信息系数(MIC)的PCA特征抽取算法,命名为YJ-MICPCA。通过YeoJohnson变换改善原始数据分布,使其近似服从高斯分布,并将PCA中计算协方差矩阵转化为计算MIC矩阵的平方,使其也能处理特征间存在的非线性关系。以UCI机器学习数据库中的11个数据集为实验对象,采用支持向量机、朴素贝叶斯模型、k近邻算法这3种分类器,比较了YJ-MICPCA与PCA及其他常用非线性降维方法LLE、Isomap、MSD、KPCA的降维效果和分类精度,结果表明YJ-MICPCA总体上优于其他几种算法。

An improved PCA algorithm for feature extraction:YJ-MICPCA

Principal component analysis (PCA) method assumes that the data obey Gaussian distribution, and it can only deal with the linear relationship between features. To address the problem, an improved PCA algorithm for feature extraction (named as YJ-MICPCA) was presented based on Yeo-Johnson transformation and maximal information coefficient (MIC). The original data distribution was changed into approximate Gaussian distribution by Yeo-Johnson transformation. Then, instead of covariance matrix in PCA, the square of MIC matrix was calculated so that YJ-MICPCA can also handle the non-linear relationship between features. Experiments on eleven datasets from UCI Machine Learning Repository were conducted, and three classifiers, i.e. support vector machine (SVM), naive Bayes model (NB) and k-nearest neighbor algorithm (k-NN), were used to compare the effect of dimensionality reduction and classification accuracy of YJ-MICPCA with PCA and such common non-linear dimensionality reduction methods as LLE, Isomap, MSD and KPCA. The results show that YJ-MICPCA is superior to other algorithms as a whole.