Principal Component Analysis And Its Application In Feature Extraction

With the development of Science and Technology, pattern recognition or pattern classification has gradually been widely used in social life. In the field of pattern recognition, feature extraction has been a key research topic, which can effectively alleviate the "curse of dimensionality" problem. Moreover, it plays an important role for recognition performance. Feature extraction has been widely applied to the fields of information processing, biometrics recognition, and text categorization. Principal component analysis belongs to feature extraction method which is common used for pattern classification in pattern recognition. In this paper, research has been done about the pre-existing principal component analysis algorithm and its improvements, a new weighted PCA method, LR-2DPCA combined with PCA algorithm and improved Euler dimensional principal component analysis algorithms are proposed. And these algorithms are applied to the sample classification and image de-noising. The main research work and innovations of the paper are as follows:A weighted PCA method which adopted the data pre-processing technology in material classification is presented. The method firstly normalizes the sample data to make the different scale data to a same range, and then calculates the weight of each sample data in the data set. Based upon that, the sample data which is processed by the technique of equalization or mean removal is multiplied by weight to highlight its importance. Finally. singular value decomposition process is utilized to realize the principal component analysis. The computer simulation results show that the proposed method can classify the data well and its advantages are obvious by comparison with tradition PCA method.Image de-noising algorithm of LR-2DPCA combined with PCA is proposed after making improvements on the principal component analysis and two-dimensional principal component analysis. The algorithm firstly extracts feature from training samples by LR-2DPCA, obtaining each row and each column characteristics which are irrelevant. Then further feature extraction is performed by PCA to obtain each pixel irrelevant features. forming the image feature space. And then reconstruction is made with main features according to the principle of the minimum reconstruction error in the feature space, so as to achieve the purpose of the face image noise reduction. The computer simulation results show that the proposed method possess certain validity and superiority in face image de-noising.A new non-linear image de-noising algorithm is formed by introducing mapping function of Euler principal component analysis to the algorithm proposed above. Firstly, the pixel values of the image are mapped to the high-dimensional feature space through a nonlinear function. And then improved two-dimensional principal component analysis algorithms is used to extract image features, forming the image feature space in which image reconstruction is processed. Finally, goes back to the pixel domain by fast angle calculation to show the image reconstruction. The computer simulation results show that the image details were better protected by nonlinear algorithm proposed. Its advantages are obvious by comparison with the algorithm proposed above.