Principle Component Analysis ( Pca ) - 1329 Words

PCA model Principle component analysis (PCA) is often used to reduce the dimensionality of a data set, and the reduced data can then explain most of the variance within the original data (Guo, Wang Louie, 2004). The main function of the PCA is to convert a number of interrelated variables into a smaller set of independent variables. The new independent variables which are called principal components (PCs). They are the linear combinations of the original variables (Jackson J.E., 2005). The PCA model can be expressed as (Miller et al., 2002): Z_ik=∑_(j=1)^pââ€"’ã€â€"G_ij H_jk ã€â€" i=1,2,†¦,m;k=1,2,†¦,n (1) Where: G_ij= the correlation of compound i with factor j H_jk= the relative impact of jth factor for the total contaminant of the kth†¦show more content†¦Standardization of the original data before the PCA can help us better understand how the variables influence the analysis (Thurston Spengler, 1985). Before applying the standardized data to the PCA, the outliers should be excluded. A sensitivity analysis should be done to determine the outliers which should be removed. The suspected outliers should be removed from the data set one at a time until the PCA reaches a stable result and the further exclusion of the samples has very little effect on the PCA results (Swietlicki et al., 1996). Outputs The output of the PCA based on Matlab includes the following: â€Å"coeff† file, â€Å"score† file, â€Å"latent† file, â€Å"tsquared† file, and the â€Å"explained† file. The â€Å"coeff† file is a matrix of the principal component coefficients, or we can call them loadings. If the input matrix is n-by-p, then the coefficient matrix should be p-by-p. The columns of the coefficient matrix represent the principal components, and the columns are placed in descending order according to the component variance. The â€Å"score† file gives us a matrix of the principal component score which represents the input matrix in the new principal component space. The score file represents the projection of theShow MoreRelatedImprove ATM Security by Face Recognition Essay1373 Words   |  6 Pagesbuzzer is connected on the FPGA board which gives instructions to the user to access the Account. If the person is not authenticated then the process is terminated and the output is show on FPGA board with the help of LEDs. Keywords- Recognition, ATM, PCA, GSM, FPGA, Euclidian distance I. INTRODUCTION The face recognition plays very important role in security system [4]. The main objective of face recognition is to recognize person from pictures or video using databases of face. There are a lots ofRead MoreFeature Extraction Essay1576 Words   |  7 Pagesmany research works, the various feature extraction algorithms are used for remotely sensed imagery. 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Henderson ID: @02181956 Spring 2007 Abstract Table of Contents Principle Component Analysis (PCA) DefinitionÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….4 Uses of PCAÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…5 Illustrative Example of PCAÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…5 Method to Determine PCAÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…..6 Basic Analysis of Variance (ANOVA) Purpose and Definition of ANOVAÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…12 Illustrative Example of ANOVAÂ…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â…Â….12 RiskRead MoreAnalysis Of Data Tri On High Dimensional And Multicollinear Data3015 Words   |  13 Pages University of Connecticut STAT5605 Project :The Analysis of Data-TRI Prediction on high-dimensional and multicollinear data â€Æ' Contents [Abstract]: 2 Section 1: Introduction 3 Section 2: Data Description 4 Section 3: Methods and Models: 5 Section 4: Analysis of Data 8 Principle Component Analysis (PCA) 8 Ridge Regression 17 Section5: Model Comparison, Conclusion and Remarks. 20 Section6: Appendix 23 Appendix.A 23 Appendix.B 27 References 29 â€Æ' [Abstract]: This paper is mainly based on the dataRead MoreA Brief Note On Surface Water And Water1557 Words   |  7 PagesSurface water (waterways, streams, and lakes) covers almost 70% of the Earth s surface are the principle wellsprings of water for mechanical, household, and watering system utilizes making it a standout amongst the most vital players in the hydrologic and biogeochemical cycles. 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