Hi,
I am considering the case where a curve is divided into multiple segments then each segment is fitted using a line that minimizes the square error. I am using the well-known dynamic program to find the best segmentation (http://people.cs.umass.edu/~sheldon/teaching/mhc/cs312/2013sp/Slides/Slides15%20-%20Segmented%20Least%20Squares.pdf ) . But I am struggling with tuning the constant that represents the cost that is multiplied by the number of segments. Is anyone aware of any heuristic to find an appropriate value for this constant apart from empirical evaluation? Thank you.
Mehiar
Hello. This is an interesting question. I had a look at the Slide 15 that you reference - it seems to end prematurely and I couldn't find the definition of the constant that you mention. Anyway, from your question, the constant trades off the overall fitting error and the number of segments. This is a classic problem in controlling complexity of representation (overfitting) with quality of approximation. In the system identification literature, there are a number of criteria including Akaike's information theoretic criterion. In practice, it is problem dependent and you will probably have to do empirical evaluation and find a "knee in the curve". This is the approach used in the link below (see references in article also).
Article Evaluation and Estimation of Various Markov Models with Appl...
Hello,
I have faced this same issue in the past. I also couldn't find a systematic way to tune the parameters. One thing I did as a starting point was to calculate the error approximating the points by just one segment. This way you can, at least, get the magnitude of the parameters you are trying to tune.
I hope it helps. (=
Hello
The problem is look like an optimization problem. So you can use any optimization algorithm to solve the problem.
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