5,544 research outputs found
Efficient estimation of AUC in a sliding window
In many applications, monitoring area under the ROC curve (AUC) in a sliding
window over a data stream is a natural way of detecting changes in the system.
The drawback is that computing AUC in a sliding window is expensive, especially
if the window size is large and the data flow is significant.
In this paper we propose a scheme for maintaining an approximate AUC in a
sliding window of length . More specifically, we propose an algorithm that,
given , estimates AUC within , and can maintain this
estimate in time, per update, as the window slides.
This provides a speed-up over the exact computation of AUC, which requires
time, per update. The speed-up becomes more significant as the size of
the window increases. Our estimate is based on grouping the data points
together, and using these groups to calculate AUC. The grouping is designed
carefully such that () the groups are small enough, so that the error stays
small, () the number of groups is small, so that enumerating them is not
expensive, and () the definition is flexible enough so that we can
maintain the groups efficiently.
Our experimental evaluation demonstrates that the average approximation error
in practice is much smaller than the approximation guarantee ,
and that we can achieve significant speed-ups with only a modest sacrifice in
accuracy
Dynamical demixing of a binary mixture under sedimentation
We investigate the sedimentation dynamics of a binary mixture, the species of
which differ by their Stokes coefficients but are identical otherwise. We
analyze the sedimentation dynamics and the morphology of the final deposits
using Brownian dynamics simulations for mixtures with a range of sedimentation
velocities of both species. We found a threshold in the sedimentation
velocities difference above which the species in the final deposit are
segregated. The degree of segregation increases with the difference in the
Stokes coefficients or the sedimentation velocities above the threshold. We
propose a simple mean-field model that captures the main features of the
simulated deposits
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