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The Common Principal Component Analyses of Multi-RCMs
FENG Jin-Ming,WANG Yong-Li,FU Cong-Bin,
FENG Jin-Ming
,WANG Yong-Li,FU Cong-Bin

大气和海洋科学快报 , 2013,
Abstract: Based on a 10-year simulation of six Regional Climate Models (RCMs) in phase II of the Regional Climate Model Inter-Comparison Project (RMIP) for Asia, the multivariate statistical method of common principal components (CPCs) is used to analyze and compare the spatiotemporal characteristics of temperature and precipitation simulated by multi-RCMs over China, including the mean climate states and their seasonal transition, the spatial distribution of interannual variability, and the interannual variation. CPC is an effective statistical tool for analyzing the results of different models. Compared with traditional statistical methods, CPC analyses provide a more complete statistical picture for observation and simulation results. The results of CPC analyses show that the climatological means and the characteristics of seasonal transition over China can be accurately simulated by RCMs. However, large biases exist in the interannual variation in certain years or for individual models.
Regression and Principal Component Analyses: a Comparison Using Few Regressors
American Journal of Mathematics and Statistics , 2012, DOI: 10.5923/j.ajms.20120201.01
Abstract: This paper uses the regression analysis and principal component analysis (PCA) to examine the possibility of using few explanatory variables to explain the variation in the dependent variable. It applied regression analysis and principal component analysis (PCA) to assess the yield of turmeric, from National Root Crop Research Institute Umudike in Abia State, Nigeria. This was done by estimating the coefficients of the explanatory variables in the analysis. The explanatory variables involved in this analysis show a multiple relationship between them and the dependent variable. A correlation table was obtained from which the characteristic roots were extracted. Also, the orthonormal basis was used to establish the linearly independent relationships of the variables. The regression analysis shows in details the constant and the coefficients of the three explanatory variables. On the other hand the principal component analysis estimates the first principal component second principal component and both components accounted for 71.4 percent of the total variation. The regression analysis and principal component analysis (PCA) yielded good estimates, which leads to the structural coefficient of the regression model. The study shows that regression analysis and principal component analysis (PCA) use few explanatory variables to explain variations in a dependent variable and are therefore efficient tools for assessing turmeric yield depending on the set objective. But that PCA is more efficient since it uses fewer variables to achieve the same result.
A review of multivariate analyses in imaging genetics  [PDF]
Jingyu Liu,Vince D. Calhoun
Frontiers in Neuroinformatics , 2014, DOI: 10.3389/fninf.2014.00029
Abstract: Recent advances in neuroimaging technology and molecular genetics provide the unique opportunity to investigate genetic influence on the variation of brain attributes. Since the year 2000, when the initial publication on brain imaging and genetics was released, imaging genetics has been a rapidly growing research approach with increasing publications every year. Several reviews have been offered to the research community focusing on various study designs. In addition to study design, analytic tools and their proper implementation are also critical to the success of a study. In this review, we survey recent publications using data from neuroimaging and genetics, focusing on methods capturing multivariate effects accommodating the large number of variables from both imaging data and genetic data. We group the analyses of genetic or genomic data into either a priori driven or data driven approach, including gene-set enrichment analysis, multifactor dimensionality reduction, principal component analysis, independent component analysis (ICA), and clustering. For the analyses of imaging data, ICA and extensions of ICA are the most widely used multivariate methods. Given detailed reviews of multivariate analyses of imaging data available elsewhere, we provide a brief summary here that includes a recently proposed method known as independent vector analysis. Finally, we review methods focused on bridging the imaging and genetic data by establishing multivariate and multiple genotype-phenotype-associations, including sparse partial least squares, sparse canonical correlation analysis, sparse reduced rank regression and parallel ICA. These methods are designed to extract latent variables from both genetic and imaging data, which become new genotypes and phenotypes, and the links between the new genotype-phenotype pairs are maximized using different cost functions. The relationship between these methods along with their assumptions, advantages, and limitations are discussed.
Super-sparse principal component analyses for high-throughput genomic data
Donghwan Lee, Woojoo Lee, Youngjo Lee, Yudi Pawitan
BMC Bioinformatics , 2010, DOI: 10.1186/1471-2105-11-296
Abstract: Here we propose a new PCA method that uses two innovations to produce an extremely sparse loading vector: (i) a random-effect model on the loadings that leads to an unbounded penalty at the origin and (ii) shrinkage of the singular values obtained from the singular value decomposition of the data matrix. We develop a stable computing algorithm by modifying nonlinear iterative partial least square (NIPALS) algorithm, and illustrate the method with an analysis of the NCI cancer dataset that contains 21,225 genes.The new method has better performance than several existing methods, particularly in the estimation of the loading vectors.Principal component analysis (PCA) or its equivalent singular-value decomposition (SVD) is widely used for the analysis of high-dimensional data. For such gene expression data with an enormous number of variables, PCA is a useful technique for visualization, analyses and interpretation [1-4].Lower dimensional views of data made possible, via the PCA, often give a global picture of gene regulation that would reveal more clearly, for example, a group of genes with similar or related molecular functions or cellular states, or samples of similar or connected phenotypes, etc. PCA results might be used for clustering, but bear in mind that PCA is not simply a clustering method, as it has distinct analytical properties and utilities from the clustering methods. Simple interpretation and subsequent usage of PCA results often depends on the ability to identify subsets with nonzero loadings, but this effort is hampered by the fact that the standard PCA yields nonzero loadings on all variables. If the low-dimensional projections are relatively simple, many loadings are not statistically significant, so the nonzero values reflect the high variance of the standard method. In this paper our focus on the PCA methodology is constrained to produce sparse loadings.Suppose X is an n × p data matrix centered across the columns, where n and p are the number of
Variable Selection Using Principal Component and Procrustes Analyses and its Application in Educational Data  [cached]
Siswadi,Achmad Muslim,Toni Bakhtiar
Journal of Asian Scientific Research , 2012,
Abstract: Principal component analysis (PCA) is a dimension-reducing technique that replaces variables in a multivariate data set by a smaller number of derived variables. Dimension reduction is often undertaken to help in describing the data set, but as each principal component usually involves all the original variables, interpretation of a PCA result can still be difficult. One way to overcome this difficulty is to select a subset of the original variables and use this subset to approximate the data. On the other hand, procrustes analysis (PA) as a measure of similarity can also be used to assess the efficiency of the variable selection methods in extracting representative variables. In this paper we evaluate the efficiency of four different methods, namely B2, B4, PCA-PA, and PA methods. We apply the methods in assessing the academic records of first year students which include fourteen subjects.
Fixing Collinearity Instability Using Principal Component and Ridge Regression Analyses in the Relationship Between Body Measurements and Body Weight in Japanese Black Cattle
A. E. O. Malau-Aduli,M. A. Aziz,T. Kojima,T. Niibayashi,K. Oshima,M. Komatsu
Journal of Animal and Veterinary Advances , 2012,
Abstract: Monthly measurements of withers height (WHT), hip height (HIPHT), body length (BL), chest width (CHWD), shoulder width (SHWD), chest depth (CHDP), hip width (HIPWD), lumbar vertebrae width (LUVWD), thurl width (THWD), pin bone width (PINWD), rump length (RUMPLN), cannon circumference (CANNCIR) and chest circumference (CHCIR) from birth to yearling age, were utilised in principal component and ridge regression analyses to study their relationship with body weight in Japanese Black cattle with an objective of fixing the problem of collinearity instability. The data comprised of a total of 10,543 records on calves born between 1937 and 2002 within the same herd under the same management. Simple pair wise correlation coefficients between the body measurements revealed positive, highly significant (P<0.001) values of 0.98 between WHT and HIPHT, HIPWD and LUVWD, while the lowest correlation of 0.50 was between CHDP and SHWD. Severe collinearity problems as portrayed by variance inflation factors (VIF) above 10 were evident in all body measurements ranging from 11.25 in PINWD to 46.94 in LUVWD except for SHWD (1.80), CHDP (3.70), CHWD (7.11) and CANNCIR (7.33). Principal component and ridge regression analyses allowed the derivation of new and more stable regression coefficients that overcame the problem of collinearity. Of all the body measurements studied, hip height was shown to be the least important for predicting the body weight of Japanese Black cattle, while SHWD and CHWD were the most important.
Clustering and Principal Component Analyses of Constraints in Smallholding Pig Keeping Systems in Manokwari, Indonesia  [cached]
DA Iyai,D Woran,I Sumpe
Journal of Animal Production , 2010,
Abstract: The research was aimed at identifying clusters and constraints on small holding pig keeping systems in Manokwari, Papua. A total of 50 pig farmers were selected purposively from 15 villages in urban and rural areas of Manokwari. Questions were focused on the constraints of small holding pig keeping systems development in Manokwari. To classify constraints, a total of seven constraints have been noted. Agglomerative hierarchical clustering (AHC) and principle component analysis (PCA) were used for clustering analysis and grouping based on components of constrains. Feeding and breeding had Eigen values of 9487 and 2010, respectively. Furthermore, Feeding and breeding had higher variability compared with other components that were 63.250 and 13.397%, respectively (Cumulative axis 1 and 2 were 76.65%). Feeding and breeding had a positive coefficient correlation (Pearson n) rF1 that could be found in some farmers in urban and rural of Manokwari. (Animal Production 12(3): 199-206 (2010) Key Words: pig, small holding systems, clustering, component analysis, development constraints, Papua
Assessing spatial genetic structure from molecular marker data via principal component analyses: A case study in a Prosopis sp. forest  [PDF]
Ingrid Teich, Aníbal Verga, Mónica Balzarini
Advances in Bioscience and Biotechnology (ABB) , 2014, DOI: 10.4236/abb.2014.52013
Abstract:

Advances in genotyping technology, such as molecular markers, have noticeably improved our capacity to characterize genomes at multiple loci. Concomitantly, the methodological framework to analyze genetic data has expanded, and keeping abreast with the latest statistical developments to analyze molecular marker data in the context of spatial genetics has become a difficult task. Most methods in spatial statistics are devoted to univariate data whereas the nature of molecular marker data is highly dimensional. Multivariate methods are aimed at finding proximities between entities characterized by multiple variables by summarizing information in few synthetic variables. In particular, Principal Component analysis (PCA) has been used to study genetic structure of geo-referenced allele frequency profiles, incorporating spatial information with a posteriori analysis. Conversely, the recently developed spatially restricted PCA (sPCA) explicitly includes spatial data in the optimization criterion. In this work, we compared the results of the application of PCA and sPCA in the study of the spatial genetic structure at fine scale of a Prosopis flexuosa and P. chilensis hybrid swarm. Data consisted in the genetic characterization of 87 trees sampled in Córdoba, Argentina and genotyped at six microsatellites, which yielded 72 alleles. As expected, principal components explained more variance than sPCA components, but were less spatially autocorrelated. The maps obtained by the interpolation of sPC1 values allowed a better visualization of a patchy spatial pattern of genetic variability than the PC1 synthetic map. We also proposed a PC-sPC scatter plot of allele loadings to better understand the allele contributions to spatial genetic variability.

Principal Component Analysis for Experiments  [PDF]
Tomokazu Konishi
Statistics , 2012,
Abstract: Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are addressed by improving the fidelity to the study design. Principal axes and the components for variables are found through the arrangement of the training data set, and the centers of data are found according to the design. By using both the axes and the center, components for an observation that belong to various studies can be separately estimated. Both of the components for variables and observations are scaled to a unit length, which enables relationships to be seen between them. Results: Analyses in transcriptome studies showed an improvement in the separation of experimental groups and in robustness to bias and noise. Unknown samples were appropriately classified on predetermined axes. These axes well reflected the study design, and this facilitated the interpretation. Together, the introduced concepts resulted in improved generality and objectivity in the analytical results, with the ability to locate hidden structures in the data.
PRINCIPAL COMPONENT AND DISCRIMINANT ANALYSES OF TRAITS OF NILE TILAPIA (OREOCHROMIS NILOTICUS) AT DIFFERENT AGES
尼罗罗非鱼(Oreochromis niloticus)不同月龄性状的主成分与判别分析

TANG Zhan-Yang,XIAO Jun,LI Li-Ping,ZHU Jia-Jie,LUO Yong-Ju,HUANG Yin,GAN Xi,
唐瞻杨
,肖 俊,李莉萍,朱佳杰,罗永巨,黄 姻,甘 西

海洋与湖沼 , 2012,
Abstract: In order to research the growth of morphological traits of Nile tilapia(Oreochromis niloticus) and judge the age matching with the size of Nile tilapia missing the best growing season,data were collected from 100 Nile tilapia at different ages individually.The body length,head length,trunk length,body depth,caudal peduncle length,caudal peduncle depth,body width and body weight were measured.The physical characteristics were analyzed by principal component and discriminant analysis.The results showed that the characteristics parameter of traits of Nile tilapia at different ages had notable correlation(P<0.05),especially the relationship between body weight and body length and body depth.The principal components of Nile tilapia at different ages were different.The first principal component is body weight factor at 2―5 months.The second principal component was caudal peduncle factor at 2―4 months,but that was trunk factor at 5-month-old.The third principal component was head factor at 2-month-old,was trunk factor at 3―4 months,was caudal peduncle factor at 5-month-old.The month age closely related to the size of Nile tilapia which had missed the best growing period was deduced by established discriminant functions,the overall discriminant accuracy was 99.25%,which was 100% 2―4 months.
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