Framework overview
The method in four steps, from one stay to a probability for each type of place.
- Candidates. Find every place (building, street piece or open space) within
R_bufferof the stay's GPS points (Candidate selection). - Scores. Give each candidate four scores, each looking at the GPS points in a different way: f_distribution, f_distance, f_temporal, f_directional.
- Utility. Add the scores together, each multiplied by a weight. The result \(V_k\) (the "utility") says how likely candidate \(k\) is. Calibration later added two more inputs, share_type and sigma.
\[V_k = w_1 f_\text{distribution} + w_2 f_\text{distance} + w_3 f_\text{temporal} + w_4 f_\text{directional}\]
The scores are added, not multiplied. With multiplication, one score of zero would remove a candidate, even if its other scores were high. 4. Probability. Turn the utilities into probabilities for each type \(t\) (building, street, open space). The model adds up \(\exp(V_k)\) for all candidates of that type and divides by the total for all candidates. This is a conditional logit model.
\[P(t \mid C_i) = \frac{\sum_{k \in t} \exp(V_k)}{\sum_{j \in \text{Candidates}(C_i)} \exp(V_j)}\]
The weights \(w\) are not chosen by hand. The model learns them from the Ground truth dataset, by finding the weights that best predict the correct answers (maximum likelihood).
Part of Assignment framework. Answers the "how" part of Research questions RQ1.