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Principal Component Analysis
 (IN PRESS, 2010). WILEY INTERDISCIPLINARY REVIEWS: COMPUTATIONAL STATISTICS, 2
, 2010
"... Principal component analysis (pca) is a multivariate technique that analyzes a data table in which observations are described by several intercorrelated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal var ..."
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Cited by 33 (5 self)
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Principal component analysis (pca) is a multivariate technique that analyzes a data table in which observations are described by several intercorrelated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the pca model can be evaluated using crossvalidation techniques such as the bootstrap and the jackknife. Pca can be generalized as correspondence analysis (ca) in order to handle qualitative variables and as multiple factor analysis (mfa) in order to handle heterogenous sets of variables. Mathematically, pca depends upon the eigendecomposition of positive semidefinite matrices and upon the singular value decomposition (svd) of rectangular matrices.
What is a Random Sequence
 The Mathematical Association of America, Monthly
, 2002
"... there laws of randomness? These old and deep philosophical questions still stir controversy today. Some scholars have suggested that our difficulty in dealing with notions of randomness could be gauged by the comparatively late development of probability theory, which had a ..."
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Cited by 4 (1 self)
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there laws of randomness? These old and deep philosophical questions still stir controversy today. Some scholars have suggested that our difficulty in dealing with notions of randomness could be gauged by the comparatively late development of probability theory, which had a
A New Data Imputing Algorithm
"... DNA microarray analysis has become the most widely used functional genomics approach in the bioinformatics field. Microarray gene expression data often contains missing values due to various reasons. Clustering gene expression data algorithms requires having complete information. This means that the ..."
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DNA microarray analysis has become the most widely used functional genomics approach in the bioinformatics field. Microarray gene expression data often contains missing values due to various reasons. Clustering gene expression data algorithms requires having complete information. This means that there shouldn't be any missing values. In this paper, a clustering method is proposed, called "Clustering Local Least Square Imputation method (ClustLLsimpute)", to estimate the missing values. In ClustLLsimpute, a complete dataset is obtained by removing each row with missing values. K clusters and their centroids are obtained by applying a nonparametric clustering technique on the complete dataset. Similar genes to the target gene (with missing values) are chosen as the smallest Euclidian distance to the centroids of each cluster. The target gene is represented as a linear combination of similar genes. Undertaken experiments proved that this algorithm is more accurate than the other algorithms, which have been introduced in the literature.
Overview Principal component analysis
"... Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several intercorrelated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal vari ..."
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Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several intercorrelated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the PCA model can be evaluated using crossvalidation techniques such as the bootstrap and the jackknife. PCA can be generalized as correspondence analysis (CA) in order to handle qualitative variables and as multiple factor analysis (MFA) in order to handle heterogeneous sets of variables. Mathematically, PCA depends upon the eigendecomposition of positive semidefinite matrices and upon the singular value decomposition (SVD) of rectangular matrices. © 2010 John Wiley & Sons, Inc. WIREs Comp Stat 2010 2 433–459 Principal component analysis (PCA) is probably the most popular multivariate statistical technique and it is used by almost all scientific disciplines. It is also likely to be the oldest multivariate technique. In fact, its origin can be traced back to Pearson1 or even Cauchy2 [see Ref 3, p. 416], or Jordan4 and also Cayley, Silverster, and Hamilton, [see Refs 5,6, for more details] but its modern instantiation was formalized by Hotelling7 who also coined the term principal component. PCAanalyzesadatatablerepresenting observations described by several dependent variables, which are, in general, intercorrelated. Its goal is to extract the important information from the data table and to express this information as a set of new orthogonal variables called principal components. PCA also represents the pattern of similarity of the observations and the variables by displaying them as points in maps [see Refs 8–10 for more details].