基于分位函数的直方图符号数据非负主成分分析法

Since the existing principal component analysis(PCA) of symbolic data mostly use some representative information instead of symbolic data, a histogram principal component analysis is proposed. Represent a histogram data by a quantile function with its characteristic, and introduce the Wasserstein distance which fully takes into account the probability distribution of the histogram data. It is easy to obtain the covariance matrix to perform the principal component analysis using this distance. However, the eigenvectors corresponding to the first m largest eigenvalues obtained by this method is not necessarily negative, so it cannot guarantee that the principal components are also quantile functions when they are represented by the quantile functions. For this point, combining the idea of DSD (distribution and symmetric distribution) regression model studied by Dias [1]et al, defining the corresponding symmetric distribution variables for each histogram variable, then obtain the non-negative principal component coefficients with the generalized covariance matrix. The experiments show the effectiveness of the algorithm. Besides, this method overcomes the disadvantage that the PCA coefficient of the histogram in [2] may be negative and retains more information of the original data.