For given coordinates, date or time the distance was calculated to each data point. Then kernels where constructed as $\mathbf{k}(\mathbf{x},x_\star)$ yielding a vector of kernels for each feature.
For given coordinates, date or time the distance was calculated to each data point according to requirements. Then kernels where constructed as $\mathbf{k}(\mathbf{x},x_\star)$ yielding a vector of kernels for each feature.
These kernels where then combined in two separate ways, first by summing the kernels and then multiplying the kernels together.
These kernels where then combined in two separate ways, first by summing the kernels and then multiplying the kernels together.
A major reason as to why the results differ is due to how each approach handles uncertainty. In the approach of adding kernels one do not care for certainty, if say the kernel value for physical distance is high but instead low for date, the data point is still considered significant. If instead multiplication is used the low date value will cause the total value to be reduced. In summary for the multiplication method a data point needs to be significant for all features to be significant in total.
A major reason as to why the results differ is due to how each approach handles uncertainty. In the approach of adding kernels one do not care for certainty, if say the kernel value for physical distance is high but instead low for date, the data point is still considered significant. If instead multiplication is used the low date value will cause the total value to be reduced. In summary for the multiplication method a data point needs to be significant for all features to be significant in total.
Measuring distances:
- Physical distance: Measured using haversine formula.
- Date: Measured in difference in days, ignoring the year.
- Time: Measured in difference of hours.
Worth noting is that for a prediction, posterior data points i.e. points that have not been measured yet is discarded.
