5.1.1 Data set (A)

Data set (A) conforms to the assumptions of the model in equation 1 and figure 2 shows the estimate of the first spatio-temporal process (spatial map 1 and time course 1 at different 'strengths' 3,2,2 for the three subjects) for tensor-PICA and PARAFAC where $R=13$ was used based on the Laplace approximation to the model order. Within the spatial, temporal and subject domain, both techniques identify the artificial signals well. For both techniques the boxplots clearly shows only a single process having high spatial correlation with the 'true' spatial map 1. In the case of PARAFAC, however, the maximum correlation is reduced, possibly an effect of suboptimal convergence. The estimation of the PARAFAC solution has used almost $15$ times the number of floating point operations compared to tensor-PICA. Estimates for the two other source processes are qualitatively similar to what is shown in figure 2.

Figure 2: Tensor-PICA and PARAFAC decomposition results for data set (A) and the first spatial map. Both for tensor-PICA and PARAFAC, $R=13$ maps were estimated, based on the Laplace approximation to the Bayesian model order. The spatial maps are normalised to unit standard deviation. The estimated time courses (blue) are shown together with the 'true' signal time courses (red), both are scaled to mean 0 and unit standard deviation. The barplots show the accuracy of the estimation in the subject domain for each of the three subjects (blue:estimated, red:true), while the boxplot shows the correlation of the 'true' spatial map with each of the $R$ estimated maps as an indicator of cross-talk between estimated maps of interest.

(i) tensor-PICA (ii) PARAFAC