Disjoint principal component analysis by constrained binary particle swarm optimization

In this paper, we propose an alternative method to the disjoint principal component analysis. The method consists of a principal component analysis with constraints, which allows us to determine disjoint components that are linear combinations of disjoint subsets of the original variables. The proposed method is named constrained binary optimization by particle swarm disjoint principal component analysis, since it is based on the particle swarm optimization. The method uses stochastic optimization to find solutions in cases of high computational complexity. The algorithm associated with the method starts generating randomly a particle population which iteratively evolves until attaining a global optimum which is function of the disjoint components. Numerical results are provided to confirm the quality of the solutions attained by the proposed method. Illustrative examples with real data are conducted to show the potential applications of the method.