LDA (Linear discriminant analysis)

Posted: 2016-09-04 , Modified: 2016-09-04

\[\begin{align} \Ga_c &= \rc{|S_c|} \sum_{i\in S_c} \ol X_i\\ \Si_c &= \rc{|S_c|} \sum_{i\in S_c} (\ol X_i - \Ga_c)(\ol X_i - \Ga_c)^T\\ \Phi &= \rc{C} \sumo cC (\Ga_c-\Ga) (\Ga_c-\Ga)^T\\ \max_{V\in \R^{k\times L}, V^TV=I_L} \fc{\Tr(V^T\Phi V)}{\Tr(V^T \sumo cC \si_c v)} &= L_1\text{ principal eigenvectors of }(\wt \Phi = \pa{\sumo cC \Si_c}^+ \Phi). \end{align}\]