关键词: 主成分分析, 广义主成分分析, 信噪比, 最大化噪声分离

Abstract:

Principal Component Analysis (PCA) is an important transform method in pattern recognition and is widely used in feature extraction and dimensionality reduction. However, since the two-dimensional images must be converted into one-dimensional vectors, there will be high dimensional data and the spatial information of pixels will be lost. Generalized Principal Component Analysis (GPCA) is the extension of PCA on two-dimensional image matrix, which does not change the location information of pixels, and its calculation cost is also significantly reduced. However, neither PCA or GPCA  considers the noise that unavoidably exists in actual images. Maximum Noise Fraction (MNF) is a transform method that is designed to decrease noise. In contrast to the maximization of variance for PCA, MNF is based on the maximization of Signal-Noise Ratio (SNR).  Similar to GPCA, this paper extends MNF on two-dimensional image matrix and proposes a Generalized Maximum Noise Fraction (GMNF) algorithm. GMNF is also based on the maximization of SNR. Meanwhile, GMNF does not lose the spatial information of pixels and has less computational complexity. Experimental results on face and hyperspectral images verify the effectiveness of the proposed algorithm.

Key words: principal component analysis;generalized , principal component analysis;signal-to-noise ratio;maximum noise fraction