Exercise:PCA in 2D

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(Step 1b: Check xRot)
 
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[[File:pca_xrot_2d.png|360px]]
[[File:pca_xrot_2d.png|360px]]
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Because Matlab/Octave could have returned <math>\textstyle -u_1</math> and/or <math>\textstyle -u_2</math> instead of <math>\textstyle u_1</math> and <math>\textstyle u_2</math>, it's also possible that you might have gotten a figure which is "flipped" or "reflected" along the <math>\textstyle x</math>- and/or <math>\textstyle y</math>-axis; this is also completely correct.
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Because Matlab/Octave could have returned <math>\textstyle -u_1</math> and/or <math>\textstyle -u_2</math> instead of <math>\textstyle u_1</math> and <math>\textstyle u_2</math>, it's also possible that you might have gotten a figure which is "flipped" or "reflected" along the <math>\textstyle x</math>- and/or <math>\textstyle y</math>-axis; a flipped/reflected version of this figure is also a completely correct result.
=== Step 2: Dimension reduce and replot ===
=== Step 2: Dimension reduce and replot ===
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In the next step, set <math>k</math>, the number of components to retain, to be 1 (we have already done this for you). Compute the resulting <math>xHat</math> and plot the results.  You should get the following (this figure should '''not''' be flipped along the <math>\textstyle x</math>- or <math>\textstyle y</math>-axis):  
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In the next step, set <math>k</math>, the number of components to retain, to be 1 (we have already done this for you). Compute the resulting <tt>xHat</tt> and plot the results.  You should get the following (this figure should '''not''' be flipped along the <math>\textstyle x</math>- or <math>\textstyle y</math>-axis):  
[[File:pca_xhat_2d.png|400px]]
[[File:pca_xhat_2d.png|400px]]
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[[Category:Exercises]]
[[Category:Exercises]]
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{{PCA}}

Latest revision as of 11:01, 26 May 2011

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