Dimensionality Reduction

• Given
  • $(x_i{)}_{i=1,\dots ,N}$ raw data points, $x_i\in {\mathbb{R}}^n$ : High dim
• To get
  • Low dim $x_i\in {\mathbb{R}}^m$ where $m<n$
• f(x) is composed of m component functions aka Features
  • $f:{\mathbb{R}}^n\to \mathbb{R}$ : scalar characteristic
  • m such Features : feature map
    • $(f_1,\dots ,f_m{)}^{\prime }=:f:{\mathbb{R}}^n\to {\mathbb{R}}^m$
    • maps input vectors to feature vectors
• KMeans
• PCA
• SOMs

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