PCA contstrained Optimization using Lagrangian Multiplier
Pre Requisite:- 1) knowledge of Co-variance Matrix 2) What is eigen vectors and values and its uses, 3) PCA Constrained Optimization of PCA using lagrangian Multiplier. Below in the picture 1 , we have the PCA formulation which is maximizing the variance, our task to find the u such that the obtained u maximizes the variance and we also have a constraint that u'u = 1, which is saying u must be a unit vector. Before , getting further in Optimizing PCA first lets learn a general case for constrained Optimization problem, General Constraint Optimization Problem for any general constraint optimization problem , given that find maximum x* for a function f(x) ...