Fig. 3.

Estimation of the number of components for the CP model, showing the mean values $(N=100)$ of the CCD, ACP, and RMSE metrics as a function of tensor rank $R$ for 100 random initializations for each stimulus condition (VIS, AUD, and AV). (a)-(b) Boxplots summarize the distribution of the mean CCD and mean ACP as a function of tensor rank. Median values are represented by black lines inside the boxplot, with the top of the whisker lines indicating the 25th and 75th percentile values. Mean values are plotted in white circles, and red circles represent outliers. Error bars represent the standard error of the mean. The plot of mean values of RSME suggests that all runs at fixed $R$ yielded the same RMSE with a standard error of the mean < 0.0001. These results suggest that all CP-ALS local minima are similar and presumably also similar to the global minimum.

(a) CCD boxplot. (b) APC boxplot. (c) Mean and standard error of the RMSE and APC as a function of tensor rank $R$.