A Genealogical Interpretation of Principal Components Analysis
نویسندگان
چکیده
منابع مشابه
A Genealogical Interpretation of Principal Components Analysis
Principal components analysis, PCA, is a statistical method commonly used in population genetics to identify structure in the distribution of genetic variation across geographical location and ethnic background. However, while the method is often used to inform about historical demographic processes, little is known about the relationship between fundamental demographic parameters and the proje...
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Principal components analysis is a well-known statistical method in dealing with large dependent data sets. It is also used in functional data for both purposes of data reduction as well as variation representation. On the other hand "handwriting" is one of the objects, studied in various statistical fields like pattern recognition and shape analysis. Considering time as the argument,...
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We consider the online version of the well known Principal Component Analysis (PCA) problem. In standard PCA, the input to the problem is a set of ddimensional vectors X = [x1, . . . ,xn] and a target dimension k < d; the output is a set of k-dimensional vectors Y = [y1, . . . ,yn] that minimize the reconstruction error: minΦ ∑ i ‖xi − Φyi‖2. Here, Φ ∈ Rd×k is restricted to being isometric. The...
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Derivation of PCA I: For a set of d-dimensional data vectors {x}i=1, the principal axes {e}qj=1 are those orthonormal axes onto which the retained variance under projection is maximal. It can be shown that the vectors ej are given by the q dominant eigenvectors of the sample covariance matrix S, such that Sej = λjej . The q principal components of the observed vector xi are given by the vector ...
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ژورنال
عنوان ژورنال: PLoS Genetics
سال: 2009
ISSN: 1553-7404
DOI: 10.1371/journal.pgen.1000686