(A) Simulated data containing three sequences in the presence of participation noise (50% participation probability). This noise condition is used for the tests in (B–F). (B) Normalized reconstruction cost () and cross-orthogonality cost () as a function of for 20 fits of these data. The cross-over point is marked with a black circle. Note that in this plot the reconstruction cost and cross-orthogonality cost are normalized to vary between 0 and 1. (C) The number of significant factors obtained as a function of ; 20 fits, mean plotted in orange. Red arrow at left indicates the correct number of sequences (three). (D) Fraction of fits returning the correct number of significant factors as a function of . (E) Similarity of extracted factors to ground-truth sequences as a function of . (F) Composite performance, as the product of the curves in (D) and (E) (smoothed using a three sample boxcar, plotted in orange with a circle marking the peak). Shaded region indicates the range of that works well ( half height of composite performance). (G–L) same as (A–F) but for simulated data containing three noiseless sequences. (M) Summary plot showing the range of values of (vertical bars), relative to the cross-over point , that work well for each noise condition ( half height points of composite performance). Circles indicate the value of at the peak of the smoothed composite performance. For each noise type, results for all noise levels from Figure 3 are shown (increasing color saturation at high noise levels; Green, participation: 90, 80, 70, 60, 50, 40, 30, and 20%; Orange, additive noise 0.5, 1, 2, 2.5, 3, 3.5, and 4%; Purple, jitter: SD of the distribution of random jitter: 5, 10, 15, 20, 25, 30, 35, 40, and 45 timesteps; Grey, timewarp: 66, 133, 200, 266, 333, 400, 466, 533, 600, and 666 max % stretching. Asterisk (*) indicates the noise type and level used in panels (A–F). Gray band indicates a range between and , a range that tended to perform well across the different noise conditions. In real data, it may be useful to explore a wider range of .