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Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
One typically uses only a subset of all the principal components for regression, making PCR a kind of regularized procedure and also a type of shrinkage estimator. Often the principal components with higher variances (the ones based on eigenvectors corresponding to the higher eigenvalues of the sample variance-covariance matrix of the ...
It is also known as Principal Coordinates Analysis (PCoA), Torgerson Scaling or Torgerson–Gower scaling. It takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a loss function called strain, [2] which is given by (,,...,) = (, (),) /, where denote vectors in N-dimensional space, denotes the scalar product between ...
The United States Constitution provides that each "House may determine the Rules of its Proceedings," [1] therefore each Congress of the United States, upon convening, approves its own governing rules of procedure. This clause has been interpreted by the courts to mean that a new Congress is not bound by the rules of proceedings of the previous ...
The Standard Code of Parliamentary Procedure classifies five "bring back" motions under the classification of main motions but lists them under the title of "Restorative Main Motions": [36] Amend a previous action, Ratify, Reconsider, Rescind, and Resume Consideration. This book treats the motion to rescind and the motion to amend something ...
Germany's principal piece of legislation concerning the legal forms and principles common to most fields [a] of its public administration is the Law on Administrative Procedure (German: Verwaltungsverfahrensgesetz, abbreviated VwVfG); before the enactment of this law in 1977, these rules had only been general principles developed in the ...
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In geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated with a ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular , and gives a constructive procedure for finding them.