# principal component analysis

**principal component analysis ( PCA)**A mathematical tool used to reduce the number of variables while retaining the original variability of the data The first principal component accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible. In interest rate risk analysis, PCA is applied to define non-parallel yield curve sifts to model. The number of variables is equal to the number of points on the yield curve, the first principal component is the rate level, the second is the twist or rotation of the yield curve around a pivot point and the third is the change in curvature or " bow" in the yield curve.__American Banker Glossary__

*Financial and business terms.
2012.*

### Look at other dictionaries:

**Principal component analysis**— PCA of a multivariate Gaussian distribution centered at (1,3) with a standard deviation of 3 in roughly the (0.878, 0.478) direction and of 1 in the orthogonal direction. The vectors shown are the eigenvectors of the covariance matrix scaled by… … Wikipedia**Principal Component Analysis**— Hauptkomponentenanalyse als Faktorenanalyse: Zwei Hauptkomponenten einer zweidimensionalen Punktwolke (orthogonal rotiert) Die Hauptkomponentenanalyse (englisch: Principal Component Analysis, PCA) ist ein Verfahren der multivariaten Statistik.… … Deutsch Wikipedia**Multilinear principal-component analysis**— (MPCA) [1] is a mathematical procedure that uses multiple orthogonal transformations to convert a set of multidimensional objects into another set of multidimensional objects of lower dimensions. There is one orthogonal transformation for each… … Wikipedia**Kernel principal component analysis**— (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are done in a reproducing kernel Hilbert space with a non linear mapping.ExampleThe two … Wikipedia**Principal components analysis**— Principal component analysis (PCA) is a vector space transform often used to reduce multidimensional data sets to lower dimensions for analysis. Depending on the field of application, it is also named the discrete Karhunen Loève transform (KLT),… … Wikipedia**Principal geodesic analysis**— In geometric data analysis and statistical shape analysis, principal geodesic analysis is a generalization of principal component analysis to a non Euclidean, non linear setting of manifolds suitable for use with shape descriptors such as medial… … Wikipedia**Component analysis**— may refer to: Principal component analysis Kernel principal component analysis Independent component analysis Neighbourhood components analysis ANOVA simultaneous component analysis Connected Component Analysis This disambiguation pag … Wikipedia**Principal component regression**— In statistics, principal component regression (PCR) is a regression analysis that uses principal component analysis when estimating regression coefficients.In PCR instead of regressing the independent variables (the regressors) on the dependent… … Wikipedia**Independent component analysis**— (ICA) is a computational method for separating a multivariate signal into additive subcomponents supposing the mutual statistical independence of the non Gaussian source signals. It is a special case of blind source separation. Definition When… … Wikipedia**Analysis**— (from Greek ἀνάλυσις , a breaking up ) is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle,… … Wikipedia