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Results tagged with pca
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user 364412
Principal component analysis (PCA) is a linear dimensionality reduction technique. It reduces a multivariate dataset to a smaller set of constructed variables preserving as much information (as much variance) as possible. These variables, called principal components, are linear combinations of the input variables.
0
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How to derive the three matrices of SVD from eigenvalue decomposition in Kernel PCA?
Based on @whuber's answer it's simply:
$$
\mathbf{V}=\mathbf{X^TU\Sigma^{-1}}
$$
- 23
1
vote
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How to derive the three matrices of SVD from eigenvalue decomposition in Kernel PCA?
Kernel PCA is usually done via eigenvalue decomposition of the Kernel Matrix $\mathbf{K}$ and standard PCA via SVD of the input $\mathbf{X}$. … In standard PCA as far as I know we can derive $\mathbf{S}$ and $\mathbf{U}$ via two eigenvalue decompositions, of the Gram and Covariance/Correlation matrices:
$$
\begin{array}{c}
X=U\Sigma V^T\\
C=\ …
- 23