PCA
From Ufldl
(→Rotating the Data) |
(→Rotating the Data) |
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<math>\textstyle u_1</math>,<math>\textstyle u_2</math>, ...,<math>\textstyle u_n</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 satisfies <math>\textstyle U^TU = UU^T = I</math> | + | One of the properties of <math>\textstyle U</math> is that it is an "orthogonal" matrix, which means |
| - | + | that it satisfies <math>\textstyle U^TU = UU^T = I</math>. | |
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 | ||
