Whitening
From Ufldl
(→2D example) |
(→ZCE Whitening) |
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nearly zero anyway, and thus can safely be dropped. | nearly zero anyway, and thus can safely be dropped. | ||
| - | == | + | == ZCA Whitening == |
Finally, it turns out that this way of getting the | Finally, it turns out that this way of getting the | ||
data to have covariance identity <math>\textstyle I</math> isn't unique. | data to have covariance identity <math>\textstyle I</math> isn't unique. | ||
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\end{align}</math> | \end{align}</math> | ||
Plotting <math>\textstyle x_{\rm ZCAwhite}</math>, we get: | Plotting <math>\textstyle x_{\rm ZCAwhite}</math>, we get: | ||
| - | + | ||
| - | + | [[File:ZCA-whitened.png]] | |
| - | + | ||
| - | + | ||
It can be shown that out of all possible choices for <math>\textstyle R</math>, | It can be shown that out of all possible choices for <math>\textstyle R</math>, | ||
this choice of rotation causes <math>\textstyle x_{\rm ZCAwhite}</math> to be as close as possible to the | this choice of rotation causes <math>\textstyle x_{\rm ZCAwhite}</math> to be as close as possible to the | ||
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When using ZCA whitening (unlike PCA whitening), we usually keep all <math>\textstyle n</math> dimensions | When using ZCA whitening (unlike PCA whitening), we usually keep all <math>\textstyle n</math> dimensions | ||
| - | of the data, and do not try to reduce its dimension. | + | of the data, and do not try to reduce its dimension. |
== Regularizaton == | == Regularizaton == | ||
