I have a dataset that contains 6 continuous variables (V1-V6), reported by participants in two conditions (A and B). For each participant, I have two lines of observations of the 6 features, corresponding to each condition (each participant has two observations of the same variable, one for each condition).

I would like to reduce these 6 features into 1 (or more) variable that best represent my data. However, I have the intuition that it is important that the algorithm "knows" about the Condition grouping factor ("random factor" in the mixed-modelling framework).

Are there any feature reduction techniques that can deal with such hierarchically nested data and take into account a grouping structure?

I've looked for "mixed principal component analysis" but didn't find much :(