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Swayam Prabha

Course Title

Multivariate Data Mining- Methods and Applications

Lecture 15

Sample PCA and Applications

By

Anoop Chaturvedi

Department of Statistics, University of Allahabad

Prayagraj (India)

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Slides can be downloaded from https://sites.google.com/view/anoopchaturvedi/swayam-prabha

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Scree plot for PC of iris data

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Example: Dataset: decathlon2 from the factoextra package of R

Athletes’ performance during two sporting events.

27 individuals (athletes) described by 13 variables (sport disciplines).

A subset of the first 23 active individuals and the first 10 active variables are selected for PCA.

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Red dashed line⇒ Expected average contribution

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PCA results for individuals (athletes): Contributions of individuals to PC1 and PC2

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BOURGUIGNON, Karpov and Clay contribute the most to both dimensions

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Average Contribution

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Example: PCA on Image Processing

The cumulative effect of the six principal components, adding one PC at a time.

R-packages: “jpeg”, "factoextra“, "gridExtra“, "ggplot2“, "magick“, "imgpalr“

The color photo has three matrices pixel by pixel, each for one component of RGB (Red, Green, Blue) color.

For converting to grayscale, sum up RGB shades and divide by max value to scale up to a maximum of 1.

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Run individual PCA on shades, R, G, and B giving an eigenvector of shades.

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Original Image

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Each color scale (R, G, B) gets its matrix and PCA.

Integrate new shades into the picture.

The image becomes clearer as we increase the number of principal components.

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