非线性二维主成分分析方法

Two-dimensional nonlinear principal component analysis:a nonlinear information compression method

提出一种矩阵数据的非线性压缩方法—非线性二维主成分分析方法.该方法在二维主成分分析的基础上,通过引入激活函数对投影后数据进行变换,从而使算法压缩性能得以提升;同时,该方法可以从网络模型角度获得直观解释,它通过在特定位置引入形变子层以改变压缩方向,最终实现对矩阵数据两个维度的同时非线性压缩;最后,设计了该模型的"形变反向传播算法",并给出了收敛性证明.数值实验基于ORL数据库的公开数据集,其结果表明:算法具有收敛性且在同等或更为苛刻的压缩条件下,非线性二维主成分分析的压缩性能优于线性主成分分析类方法,包括主成分分析,二维主成分分析及广义主成分分析.

In this paper, a new technique named two-dimensional nonlinear principal component analysis(2DNPCA) is developed for information compression. It can be viewed as a generalization of the principal component analysis(PCA), two-dimensional PCA(2DPCA) or generalized PCA(GPCA).Our work mainly includes the following three aspects: the first and foremost, activation function is introduced to transform the projected data so as to achieve nonlinear compression of data;in the second place, we add deformable sub-layers into network model to change the compression direction, so that matrix data can be compress on both sides simultaneously;the last but not the least, the deformable back propagation(DBP) algorithm adapted to 2DNPCA is designed and it is proved to be convergent.The experimental results show that 2DNPCA is superior to PCA, 2DPCA and GPCA in compression efficiency. Supplementary materials for this article are available online.