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Formatting headers and lists
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ehumph committed Apr 8, 2022
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2 changes: 1 addition & 1 deletion 04-overview.Rmd
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# (PART\*) DIMENSIONALITY REDUCTION OVERVIEW {-}
# Introduction

## The difficulties of high-dimensional datasets

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30 changes: 19 additions & 11 deletions 05-student-guide.Rmd
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```

The `prcomp()` command will create a list containing multiple dataframes and vectors:
-_sdev_, a vector of the standard deviations for each PC
-_rotation_, a matrix of the eigenvectors for each variable
-_center_, a vector of the center value for each variable
-_scale_, a vector of the scaling factor for each variable
-_x_, a matrix of the individual PC values for each flower

*_sdev_, a vector of the standard deviations for each PC

*_rotation_, a matrix of the eigenvectors for each variable

*_center_, a vector of the center value for each variable

*_scale_, a vector of the scaling factor for each variable

*_x_, a matrix of the individual PC values for each flower


## Choosing the number of PCs
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The size and position of the vectors (arrows) in the correlation circle can tell us quite a lot about the variables.

-Positively correlated variables are grouped together.
-Negatively correlated variables are positioned on opposite sides of the plot origin (opposed quadrants) .
*Positively correlated variables are grouped together.

*Negatively correlated variables are positioned on opposite sides of the plot origin (opposed quadrants) .

-Vectors that end close to the circle outline greatly contribute to a given PC.
-Shorter vectors contribute very little.
*Vectors that end close to the circle outline greatly contribute to a given PC.

*Shorter vectors contribute very little.

-Vectors that are primarily horizontal mostly contribute to the first PC (the x-axis).
-Vectors that are more vertical contribute primarily to the second PC (the y-axis).
*Vectors that are primarily horizontal mostly contribute to the first PC (the x-axis).

*Vectors that are more vertical contribute primarily to the second PC (the y-axis).


## Visualizing structure using PCs
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