 Application Center - Maplesoft

# Principal Component Analysis

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Samir Khan

 Introduction Principal Component Analysis transforms a multi-dimensional data set to a new set of perpendicular axes (or components) that describe decreasing amounts of variance in the data.     This worksheet performs a principal component analysis on multi-dimensional data. Those components that have the least impact on the variance can be discarded, and the simplified data reconstructed from the remaining components.

 >     Specify Data

 > Number of components to keep

 > Centre the Data

 >  >  Calculate the Covariance, Eigvenvalues and Eigenvectors

Covariance Matrix

 > Eigenvectors and eigenvalues

 >  Sorting the eigenvectors in order of decreasing eigenvalues (i.e. the most significant eigenvvectors are first)

 > > Calculate the Princpal Components

The feature contains the retained components

 > Hence the data in terms of the new coordinate system.

 > Reconstruct Data from Principal Components

 >  > Plot Reconstruct Data

 >  >  > 