Algorithm on trajectory analysis.

Question

Hello, I would like to analyse trajectory data based on given templates. I need to stack similar trajectories together. The data is a set of coordinates (xy, xy, xy) and the templates are again lines defined by the set of control points.

I don't know to what direction to go, maybe to Neural Networks or pattern recognition?

Could you please recommend a page, book or library to start with?

Kind regards, Arman.

PS: Is it the right place to ask the question? EDIT To be more precise the trajectory contains about 50-100 control points. Here you can see the example of trajectories: http://www.youtube.com/watch?v=KFE0JLx6L-o

Answer 1

Your question is a quite vague.

You can use regression analysis (http://en.wikipedia.org/wiki/Regression_analysis) to find the relationship between x and y on a set of coordinates, and then compare that with other of trajectories.

Are there always four coordinates per trajectory? You might want to calculate the euclidian distance between the first coordinates of all trajectories, and then the same for the second and so on.

You might want to normalize the distance and analyze the change in direction instead. It all comes down to what you really need.

If you need to stack similar trajectories together you might be interested in the k-nearest neighbour algorithm (http://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm). As for the dimensions to use for that algorithm, you might use your xy coordinates or any derivates.

Answer 2

You can use a clustering algorithm to 'stack the similar trajectories together'. I have used spectral clustering on trajectories with good results. Depending on your application hierarchical clustering may be more apropriate.

A critical part of your analysis will be the distance measure between trajectories. State of the art is dynamic time warping. I've also seen good results achieved with a modified Hausdorff measure.