Theory of fractional covariance matrix and its applications in PCA and 2D-PCA

作者：

Highlights：

• We extend fractional covariance matrix (FCM) to fractional order forms by the given new definition.

• We propose two new techniques of dimensionality reduction by using FCM to PCA and 2D-PCA.

• Two new techniques are superior to the standard PCA and 2D-PCA if choosing different order between 0 and 1, which expands the transition recognition ranges of PCA and 2D-PCA.

摘要

•We extend fractional covariance matrix (FCM) to fractional order forms by the given new definition.•We propose two new techniques of dimensionality reduction by using FCM to PCA and 2D-PCA.•Two new techniques are superior to the standard PCA and 2D-PCA if choosing different order between 0 and 1, which expands the transition recognition ranges of PCA and 2D-PCA.

论文关键词：Fractional variance,Fractional covariance,Fractional covariance matrix,FPCA,2D-FPCA

论文评审过程：Available online 6 April 2013.

论文官网地址：https://doi.org/10.1016/j.eswa.2013.03.048