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I developed a new route prediction algorithm and I am trying to find a metric that informs on how well a prediction was.

This metric is meant to be used offline, meaning that the goal is not to measure the quality of the prediction when it is need in real time. Instead, We are given a set $R=\{r_1,r_2,...r_{|R|}\}$ of routes that occurred in the past and for each $r_i\in R$ we take a small prefix of $r_i$ and provide it as input to the algorithm which in turn outputs a prediction route $p_i$.

Therefore, given the set $R=\{r_1,r_2,...r_{|R|}\}$ and the corresponding predictions set $P=\{p_1,p_2,...p_{|P|}\}$, I want to compare each pair of routes $(p_i,r_i)$ to determine how different $p_i$ is from $r_i$.

Can anyone point me in the right direction?

My first idea was to compute the area comprised between the two routes $p_i$ and $r_i$, but I really do not know how to interpret the output in terms of good or bad result.

Thanks for the attention

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    $\begingroup$ You may consider the Frechet Distance as explained here. Other answers mentioned here may also be relevant. $\endgroup$ – user12075 Jan 9 at 19:00
  • $\begingroup$ How do you store your routes? Do you use x and y coordinates? Are the data points synchronized in time? Do they have the same length? $\endgroup$ – MachineLearner Jul 9 at 18:39
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You need to define what a "quality route" is in the context of your problem and score based on that. This will likely be something along the lines of the total distance of the route, the expected time to traverse the route, the expected fuel/resource consumption required to complete the route, or some combination of these. You presumably want to predict routes that are as good or better than the routes given in your set R: you need to define what it means for a route to be "better."

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Check: A survey of evaluation methods for personal route and destination prediction from mobility traces

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