$k$-modes Correspondence Analysis

Choice of metrics offer the possibility to perform generalisations of established multivariate methods. An interesting one for pharmaco-EEG data is a generalisation of correspondence analysis. The purpose of this analysis of a multiple contingency table is to break down the whole $\chi^2$ statistic as the sum of squared singular values which are associated with Principal Tensors giving a description of lack of independence. Although usually applied to contingency data, a correspondence analysis approach is valid here as each cell is a measure of energy amplitude according to a particular frequency band, a particular lead, a particular time, etc..., so the whole count and marginals have a meaning of energy amplitude. The literature has been abundant regarding correspondence analysis methods for more than two variables but usually looks at two by two lack of independence and not the lack of complete independence. Using the PTA-$k$modes framework the extension from $2$ to $k$ variables is straightforward the analysis of the lack of complete independence.