Area-based Principal Component Analysis And Application

Feature extraction is a key issue in image recognition.Principal component analysis(PCA)and two-dimensional principal component analysis(2DPCA)are the two most representative methods for Feature extraction.However,the most existing PCA and 2DPCA methods use the square of the Euclidean distance to measure which results in the sensitivity to noise,moreover,they do not explicitly consider the reconstruction error and do not take into account the relationship between reconstruction error and variance of projected data,which reduce the flexibility of the algorithm.Therefore,starting from the above problems,this paper studies the Area PCA and matrix-based Area PCA.The main content of the paper is as follows:1.For existing PCA methods are not robust to outliers and cannot effectively consider the relationship between the data reconstruction error and variance,which results in low flexibility,this paper studies a vector-based area principal component analysis,namely Area PCA.Area PCA uses the L2 norm to measure the reconstruction error and variance of the data and minimize the summation of area between projection directions and reconstruct error of each data.Compared with some robust PCA methods,Area PCA is not only robust to outliers,but also retains rotational invariance and other nice property of traditional PCA.To better solve Area PCA,we use an iterative algorithm that makes the algorithm have a closed-form solution in each iteration.Experimental results on AR,Extended Yale B,and PIE databases verify the effectiveness of our proposed algorithm.2.Area PCA is a feature extraction algorithm based on one-dimensional vectors and cannot well exploit the spatial structure information that is embedded in pixels.In view of the deficiencies of Area PCA,this paper studies a matrix-based area principal component analysis,namely Area 2DPCA.Area 2DPCA is a two-dimensional extension of Area PCA.The algorithm uses F-norm to characterize the variance and reconstruction error in the criterion function.It is not only robust to outliers,but also retains rotational invariance and other nice property of traditional 2DPCA.The experimental results on AR,Extended Yale B,PIE and other databases verify the effectiveness of our proposed algorithm.