# Principal Component Analysis PCA Markku HautaKasari Jussi Parkkinen

• Slides: 23

Principal Component Analysis (PCA) Markku Hauta-Kasari Jussi Parkkinen University of Joensuu Color Group FINLAND

Algorithm 1. 2. 3. 4. Calculate correlation matrix for the data set Calculate eigenvalues and eigenvectors for the correlation matrix Select eigenvectors corresponding to the largest eigenvalues as a new basis for the data set Calculate principal components between eigenvectors and the data set Applications: compression, pattern recognition etc. Frequently used for spectral image data

An example on calculating the PCA Example on PCA for the data set of 2 dimensional vectors

Spectral Images & Principal Component Analysis (PCA) spectrum 1. calculating correlation matrix and eigenvectors, selecting base vectors 2 -D spectral image Matrix B needs to be transposed 2. calculating inner product images 3. reconstructing spectral image

Illustration of PCA base vectors B original spectral image S 1. 2. inner product images P

Illustration of PCA base vectors B ~ reconstructed spectral image S 3. inner product images P

An example of the PCA for the spectral image of printed product

Eigenvectors in case of the pure radiance data

Eigenvectors in case, in which the data is multiplied by a spectral sensitivity of a human eye and by the used light source

Inner-product images between the spectral images and eigenvectors Inner-product images between eigenvectors and data, which is multiplied by a spectral sensitivity of a human eye and the used light source

An example of the PCA for the spectral image measured from the PDA-display

Sample spectral images of a PDA-display

Light sources PDA display and external illumination

Inner-product images between the spectral images and eigenvectors Corresponding eigenvectors

Inner-product images between eigenvectors and data, which is multiplied by a spectral sensitivity of a human eye and by the used light source Corresponding eigenvectors

Inner-product images between the spectral images and eigenvectors Corresponding eigenvectors

Inner-product images between eigenvectors and data, which is multiplied by a spectral sensitivity of a human eye and by the used light source Corresponding eigenvectors

Summary PCA can be effectively used for spectral image compression PCA can be used for pattern recognition tasks Exercises on implementing the PCA