Figure 11

Measurement of crowd behavior. A set of 3 features is defined in order to numerically evaluate the behavior of the crowd. These features are based upon the set of local optima of the completion time series which measures the global achievement of a puzzle. This time series (black dots) is highly noisy and in order to focus on overall behavior the time series is first smoothed (green line) prior to finding the local optima. Local optima indicate remarkable points of the time series whose position in time and value summarize the progress and the efficiency of the crowd (local maxima are orange, local minima are yellow). We further refine this information into three measures to capture crowd behavior: ${\mathrm{\Delta }}_{\mathrm{completion}}$ the difference in completion between an optima and the next optima, ${\mathrm{\Delta }}_{\mathrm{time}}$ the difference in time between an optima and the next optima, and ${\mathrm{\Delta }}_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}}$ the difference in time between a local maxima and the moment at which the completion reaches back for the first time the same level as the maxima (indicated in purple for the first maxima of the figure). The local optima are local within a windows of a given size, as a consequence not all optima are included in the final features. Details about the choice of a particular local optima size are given in Figure 12.