Dimensionality reduction via hierarchical factorial structure

Manifold multidimensional concepts are explained via a tree-shape structure by taking into account the nested hierarchical partition of variables. The root of the tree is a general concept which includes more specific ones. In order to detect the different specific concepts at each level of the hierarchy, we can identify two different features regarding groups of variables: the internal consistency of a concept and the correlation between concepts. Thus, given a data positive correlation matrix, we reconstruct the latter via an ultrametric correlation matrix which detects hierarchical concepts by looking for their internal consistency and the correlation between them measured by relative indices.