基于矩阵完备投影的快速主分量分析算法

A New Method of Fast-complete Matrix-projection Principal Component Analysis

主分量分析是模式识别中经常采用的一种方法,但是由于经典的主分量分析在处理图像矩阵需要将图像展开成向量形式,因而造成其协方差矩阵维数和计算量太大,同时由于没有注意到图像矩阵中像素之间空间相关性,使得抽取的图像特征并不是优秀的,为此提出了一种基于矩阵完备投影的快速主分量分析算法(FMPCA),该算法不仅大大降低了分析过程中的计算量,而且发挥了图像矩阵行和列之间的空间特性,从而提高了整体性能。通过对NUST603、Yale和ORL图像库进行的实验证明,该算法不仅具有快速提取图像特征的能力,而且综合性能优于相应的一些主分量分析方法。

Principal component analysis （PCA） is a well-known method in pattern recognition. But the classical PCA transforms original image matrices into same dimensional vectors which will result in very large dimension of covariance matrix and very high computational complexity when processing image matrices. Moreover, extracted feature of the images are not excellent due to the fact that the pixel＇s spatial relativity based on the classical PCA was neglected. This paper presents a fast-complete matrix-projection principal component analysis （FMPCA） that decreases the computational complexity and utilizes the spatial relativity between rows and columns. The experiments conducted on NUST603, Yale and ORL face database demonstrate that the proposed algorithm can not only extract image feature efficiently but also maintain more powerful and excellent performance than some other principal component analysis methods.