[PS] Examples II

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}