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b/semester6/iml/parts/08_unsupervised.tex index 13646bb..ecc0fe0 100644 --- a/semester6/iml/parts/08_unsupervised.tex +++ b/semester6/iml/parts/08_unsupervised.tex @@ -174,6 +174,12 @@ There are several other methods to do this, based e.g. on concepts from informat {\footnotesize \textbf{Intuition}: High dimensional data usually has many redundancies \& highly correlated features. Dimensionality Reduction in practice preserves most substantial data. This idea is formalized as the \textit{Manifold Hypothesis}. + + \remark \textbf{Requirement}: We assume $\mathbf{X}$ is centered. For general $\mathbf{X}$, we therefore use: + $$ + \bar{\mathbf{X}} = \mathbf{X} - \mathbf{I}\mu \qquad \mu = \sum_{i=1}^{n}x_i + $$ + i.e. we subtract the mean $\mu$ of all $x_i$ from each $x_i$. } \subsubsection{PCA in one dimension}

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