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I have a tracker that outputs the trajectory $(x,y,z)$ of an object (e.g., a can).

I want to use these trajectories to train a classifier (i.e., SVM) in order to infer the activity that the person manipulating the object is performing (e.g., drinking from a can or pouring from a can )

Which kind of features should I use to quantize these trajectories?

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Just some quick ideas from someone who works in the realm of feature extraction in physical systems modeling such as this: you want to find the simplest and strongest differentiating characteristics of the different behaviors you're interested in classifying.

First, though: do you know in advance the full extent of behaviors you wish to classify? If not, the problem will be much harder. If you do, then brainstorm the key non-overlapping differences. Alas, you mention drinking and pouring, but drinking is a subset of pouring where the target is the drinker's mouth. So you might need some distinguishing characteristics from the data such as the height of the can in absolute space (unless you are allowing for people drinking while sitting, etc. etc.). As you see, assumptions and context are everything in tackling these problems, and expecting to classify human behavior based on a single trajectory of three numbers does not sound like a robust way to solve a problem, as stated.

More importantly then, you should consider what is the ultimate problem you're actually trying to solve? What else can you measure or know about the situation?

If you know more about the context, possible features might include measures of the linearity of the trajectory or, conversely, radius of curvature in the trajectory. Also, measure the amount of rotation of the can (but do you just have a single point? In which case you've already lost a valuable feature...), or look for clusters of different patterns of motion and rotation through time, and split up your trajectory into piecewise segments. But none of this is helpful if you don't understand a lot more about the context of what you're trying to solve.

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