To fill in gaps in the City of Toronto's count program in order to provide a complete picture of volumes across the entire city.
Several methods are tested for this purpose and are detailed below.
-
Average of Nearest Neighbours (confidence code = 3)
Nearest neighbours: 5 (or less) segments of the same road class that are maximum 300m (nearest point to point distance) away from the target segment -
Linear Regression (Based on Proximity only) (confidence code = 4)
Take the volumes of the nearest 5 segments of the same road class as dependent variables (ordered by proximity). -
Linear Regression (Directional) (confidence code = 2)
Take the volumes of the nearest 2 parallel segments and 2 perpendicular segments as dependent variables. -
Kriging
Implemented using the Gaussian Process model from scikit-learn
Input: (4-dimensional) from_x, from_y, to_x, to_y (coordinate information from the start and end of the segment)
Output: volume
Covariance matrix is constructed based on the coordinate information of the segments in order to find the spatial correlation of volumes.
- | Linear Regression (proximity only) | Direction Linear Regression | Average of Nearest Neighbours |
---|---|---|---|
Scatter plot | ![]() |
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Root Mean Squared Error | 4374 | 4232 | 4554 |
Coef. of Det. | 0.480 | 0.542 | 0.492 |
- | Linear Regression (proximity only) | Direction Linear Regression | Average of Nearest Neighbours |
---|---|---|---|
Scatter plot | ![]() |
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Root Mean Squared Error | 2285 | 2143 | 2067 |
Coef. of Det. | 0.345 | 0.461 | 0.341 |
- | Linear Regression (proximity only) | Direction Linear Regression | Average of Nearest Neighbours |
---|---|---|---|
Scatter plot | ![]() |
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Root Mean Squared Error | 1349 | 1263 | 1233 |
Coef. of Det. | 0.312 | 0.268 | 0.364 |
- | Linear Regression (proximity only) | Direction Linear Regression | Average of Nearest Neighbours |
---|---|---|---|
Scatter Plot | ![]() |
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Root Mean Squared Error | 736 | 732 | 718 |
Coef. of Det. | 0.230 | 0.046 | 0.213 |
Road Class | Perpendicular Segs Coef | Parallel Segs Coef |
---|---|---|
Major Arterials | 0.0077 -0.0013 | 0.4404 0.4340 |
Minor Arterials | -0.0132 0.0429 | 0.4129 0.2954 |
Collectors | 0.0104 0.0249 | 0.3937 0.1681 |
Locals | 0.0037 0.0129 | 0.1779 0.2441 |
The coefficients indicate a strong correlation between upstream and downstream segments and a week if existent relationship between perpendicular segments. As we move from major arterials to locals, the relationship gets messier.
Road Class | Semivariogram |
---|---|
Major Arterial | ![]() |
Minor Arterial | ![]() |
Collector | ![]() |
The relationship between distance and volume relationship is weak. The variance does not fit any model very well. A Gaussian Process Kriging model was fitted to each road class anyway and the results are inferior than regression. Therefore kriging is not used in actual implementation.
Road Class | Method |
---|---|
Major Arterials | Directional Linear Regression |
Minor Arterials | Directional Linear Regression |
Collectors | Average of Neighbours |
Locals | Average of Neighbours |
Note that expressways are not included. However, there are uncounted expressways that need to be included in the future.