# Principal Components Analysis - Teradata Warehouse Miner

## Teradata Warehouse Miner User Guide - Volume 3Analytic Functions

Product
Release Number
5.4.5
Published
February 2018
Language
English (United States)
Last Update
2018-05-04
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yuy1504291362546.ditamap
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B035-2302
Product Category
Software

The goal of principal components analysis (PCA) is to account for the maximum amount of the original data’s variance in the principal components created. Each of the original variables can be expressed as a linear combination of the new principal components. Each principal component in its turn, from the first to the last, accounts for a maximum amount of the remaining sum of the variances of the original variables. This allows some of the later components to be discarded and only the reduced set of components accounting for the desired amount of total variance to be retained. If all the components were to be retained, then all of the variance would be explained.

A principal components solution has many desirable properties. First, the new components are independent of each other, that is, uncorrelated in statistical terminology or orthogonal in the terminology of linear algebra. Further, the principal components can be calculated directly, yielding a unique solution. This is true also of principal component scores, which can be calculated directly from the solution and are also inherently orthogonal or independent of each other.