5.1.5 Data set (E)

In data set (E), all signals are temporally and spatially inconsistent between subjects. While each subject contains each of the spatial maps and time courses in figure 1, the association between true spatial maps and true time courses differs in each subject. Figure 6 shows the results for one of the source signals. Despite the fact that the signal content in this data set does conform to the tri-linear model, the high degree of collinearity in this representation prevents PARAFAC from clearly identifying the source process in the spatial or temporal domain. The tensor-PICA results contain exactly one source with high spatial correlation for each of the three 'true' spatial maps (only one of the maps is shown, the results for spatial map 1 and 2 are qualitatively similar). The estimated subject-factor differs significantly from the 'true' relative activation strengths. Also, the associated time course only explains $46.26\%$ of the final amount of variance among the set of 3 time-courses, indicating that a rank-1 approximation might not be sufficient to capture the temporal dynamics.

Figure 6: Tensor-PICA and PARAFAC decomposition results for data set (E) and estimated spatial map 3.

(i) tensor-PICA (ii) PARAFAC