Figure 1
From: Highlighting nonlinear patterns in population genetics datasets
MCE computes distances between individuals (given a selected norm; in our case, the Euclidean norm) in G to generate the matrix of pairwise distances A.
This matrix can be thought of as the adjacency matrix representation of a fully connected graph whose edges are weighted by inter-individual distances. A MST T is extracted from this graph and distances between individuals are re-computed over it to obtain the MC-kernel D. In this paper, we used a version of MCE in which D is non-centred and the economy-size singular value decomposition is applied to it to determine the coordinates of each individual in a space of dimension d. This version of MCE is also known as ncMCE. The power of this approach relies on the MC-kernel. The MST T is a graph that extracts a greedy path that summarises the main relational information between the features of the dataset. This graph avoids noise and spurious information and emphasises the nonlinear relationship between the most representative and informative features of the data samples8,9,15,24.
