PCA
From Ufldl
(→PCA on Images) |
(→Rotating the Data) |
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This is the training set rotated into the <math>\textstyle u_1</math>,<math>\textstyle u_2</math> basis. In the general | This is the training set rotated into the <math>\textstyle u_1</math>,<math>\textstyle u_2</math> basis. In the general | ||
case, <math>\textstyle U^Tx</math> will be the training set rotated into the basis | case, <math>\textstyle U^Tx</math> will be the training set rotated into the basis | ||
- | <math>\textstyle u_1</math>,<math>\textstyle u_2</math>, | + | <math>\textstyle u_1</math>,<math>\textstyle u_2</math>, ...,<math>\textstyle u_n</math>. |
- | One of the properties of <math>\textstyle U</math> is that it | + | One of the properties of <math>\textstyle U</math> is that it satisfies <math>\textstyle U^TU = UU^T = I</math>; |
+ | another way of saying this is that <math>U</math> is an "orthogonal" matrix. | ||
So if you ever need to go back from the rotated vectors <math>\textstyle x_{\rm rot}</math> back to the | So if you ever need to go back from the rotated vectors <math>\textstyle x_{\rm rot}</math> back to the | ||
original data <math>\textstyle x</math>, you can compute | original data <math>\textstyle x</math>, you can compute |