How to map a trajectory to a vector?

I have a series of data points in this form (timestamp, lat, long) for a set of users. Each user has a trajectory when he travels from point A to point B. There might be any number of points from A to B. They are ordered data points based on time stamp. I want to transform them as a vector to do various analysis tasks. One thought I have is to look at turns and make them as a dimension. I would like to know more approaches.
What I want is a one vector representing the whole trajectory, think of it like one point for a trajectory.Right now I have a collection of 3d points.

I would like to do trajectory similarity search. If there are two trajectories that in time are travelling close to each other then they are similar. Think of it like this you are going from house to work at 9am. Somebody else at 9:10 am also his home for work and stays some distance from you. Since u have the same workplace , you will most likely have same trajectory. Something like a classifier built on top of a trajectory. I can do activity detection in a trajectory, I can do a source destination analysis too.

Answer

I would start with dynamic time warping. As long as you have the distance between any two points (lat,long) this approach should work. It adjusts for different speeds of motion. For instance, you and I live in the same village and go to work to the same factory, but I stop by a coffee shop on the way. It takes longer for me to arrive but we’re more or less on the same path, so the similarity measure adjusts for different time scales.

This is different from what you have in mind. It seems that you want to come up with one value (vector) to represent the trajectory, then calculate the distance between the vectors. I’m suggesting you to use the distance measure between the trajectories directly, without intermediate step.

Attribution
Source : Link , Question Author : gizgok , Answer Author : Aksakal

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