PCA
From Ufldl
(→Example and Mathematical Background) |
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\Sigma = \frac{1}{m} \sum_{i=1}^m (x^{(i)})(x^{(i)})^T. | \Sigma = \frac{1}{m} \sum_{i=1}^m (x^{(i)})(x^{(i)})^T. | ||
\end{align}</math> | \end{align}</math> | ||
| - | If <math>\textstyle x</math> has zero mean, then <math>\textstyle \Sigma</math> is exactly the covariance matrix of <math>\textstyle x</math>. | + | If <math>\textstyle x</math> has zero mean, then <math>\textstyle \Sigma</math> is exactly the covariance matrix of <math>\textstyle x</math>. (The symbol "<math>\textstyle \Sigma</math>", pronounced "Sigma", is the standard notation for denoting the covariance matrix. Unfortunately it looks just like the summation symbol, as in <math>\sum_{i=1}^n i</math>; but these are two different things.) |
It can then be shown that <math>\textstyle u_1</math>---the principal direction of variation of the data---is | It can then be shown that <math>\textstyle u_1</math>---the principal direction of variation of the data---is | ||
