A: The DPA uses pre-defined groups in your dataset, such as colour groups in ioGAS, and determines a linear projection that maximises the separation between the groups. i.e. samples from the same group are projected very close to each other and the means of each group are as far apart as possible. To take into account any correlations that exist within a group, the DPA function takes into account the variability or scatter within each group. It is this matrix that needs to be inverted to determine the projection. In this sense, if the W matrix is singular it is because there is no within-group variation with one of the elements being used. This is represented by a near-zero or very low determinant of the W matrix. To resolve this message, the distribution of the data will need to be investigated to see if there is any column with little to none within group variation.