Local Space-Time Smoothing for Version Controlled Documents
Figure 4: Test set error rate and F1 measure for edge prediction (section boundaries in Wikipedia articles and author change in Google Wave). The space-time domain Ω was divided to a grid with each cell labeled edge (y=1) or no edge (y=0) depending on whether it contained any edges. Method a corresponds to a predictor that always selects the majority class. Method b corresponds to the TextTiling test segmentation algorithm [Hearst1997] without paragraph boundaries information. Method c corresponds to a logistic regression classifier whose feature set is composed of statistical summaries (mean, median, max, min) of ˙γs(s,t) within the grid cell in question as well as neighboring cells.
['[BOLD] Article', '[BOLD] Rev.', '[BOLD] Voc.  [BOLD] Size', '[ITALIC]  [BOLD] p [BOLD] ( [ITALIC]  [BOLD] y [BOLD] )', '[BOLD] Error Rate a', '[BOLD] Error Rate b', '[BOLD] Error Rate c', '[BOLD] F1 Measure a', '[BOLD] F1 Measure b', '[BOLD] F1 Measure c']
controlled Wikipedia articles Religion and Atlanta. The local gradient maxima nicely match the segment boundaries which lead us to consider training a logistic regression classifier on a feature set composed of gradient value statistics (min, max, mean, median of ∥˙γs(s, t)∥ in the appropriate location as well as its neighbors (the space-time domain Ω was divided into a finite grid where each cell either contained an edge (y=1) or did not (y=0)). We conclude from the figure that the gradient information leads to better prediction than TextTiling (on both accuracy and F1 measure).