Marginal probability distribution estimation in characteristic space of covariance-matrix

Marginal probability distribution has been widely used as the probabilistic model in EDAs because of its simplicity and efficiency. However, the obvious shortcoming of the kind of EDAs lies in its incapability of taking the correlation between variables into account. This paper tries to solve the problem from the point view of space transformation. As we know, it seems a default rule that the probabilistic model is usually constructed directly from the selected samples in the space defined by the problem. In the algorithm CM-MEDA, instead, we first transform the sampled data from the initial coordinate space into the characteristic space of covariance-matrix and then the marginal probabilistic model is constructed in the new space. We find that the marginal probabilistic model in the new space can capture the variable linkages in the initial space quite well. The relationship of CM-MEDA with Covariance-Matrix estimation and principal component analysis is also analyzed in this paper. We implement CM-MEDA in continuous domain based on both Gaussian and histogram models. The experimental results verify the effectiveness of our idea.