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| data_mining:pca [2014/08/24 01:55] – [Algorithmus] phreazer | data_mining:pca [2014/08/24 02:10] – [Parameterwahl (k)] phreazer | ||
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| $z = U_{\text{reduce}}^T x$ | $z = U_{\text{reduce}}^T x$ | ||
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| + | ===== Parameterwahl (k) ===== | ||
| + | |||
| + | 99% der Varianz bleibt erhalten. | ||
| + | |||
| + | $$ | ||
| + | \frac{\frac{1}{m} \sum_{i=1}^m || x^{(i)} - x_{\text{approx}}^{(i)} ||^2}{\frac{1}{m} \sum_{i=1}^m || x^{(i)}||^2} \leq 0.01 | ||
| + | $$ | ||
| + | |||
| + | [U,S,V] mit S als diagonale Matrix. | ||
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| + | Für ein k, kann $1-\frac{\sum_{i=1}^k S_{ii}}{\sum_{i=1}^n S_{ii}} \leq 0.01$. | ||
| + | |||
| + | ===== Decompression ===== | ||
| + | $x_\text{approx} = U_\text{reduce} z$ | ||