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POSegmented least squares algorithm, don't understand this dynamic programming concept at all
 

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    <p>I've been trying to implement this algorithm in Python for a few days now. I keep coming back to it and just giving up and getting frustrated. I don't know whats going on. I don't have anyone to ask or anywhere to go for help so I've come here. </p> <p>PDF Warning: <a href="http://www.cs.uiuc.edu/class/sp08/cs473/Lectures/lec10.pdf" rel="noreferrer">http://www.cs.uiuc.edu/class/sp08/cs473/Lectures/lec10.pdf</a></p> <p>I don't think its a clearly explained, I sure don't understand.</p> <p>My understanding of what's happening is this:</p> <p>We have a set of of points (x1,y1), (x2,y2).. and we want to find some lines that best fit this data. We can have multiple straight lines, and these lines come from the given forums for a and b (y = ax +b). </p> <p>Now the algorithm starts at the end (?) and assumes that a point p(x_i, y_i) is part of the line segment. Then the notes say that the optimal solution is 'is optimal solution for {p1, . . . pi−1} plus (best) line through {pi , . . . pn}'. Which just means to me, that we go to the point p(x_i, y_i) and go backwards and find another line segment through the rest of the points. Now the optimal solution is both these line segments. </p> <p>Then it takes a logical jump I can't follow, and says "Suppose the last point pn is part of a segment that starts at p_i. If Opt(j) denotes the cost of the first j points and e(j,k) the error of the best line through points j to k then Opt(n) = e(i, n) + C + Opt(i − 1)"</p> <p>Then there is the pseudocode for the algorithm, which I don't understand. I understand that we want to iterate through the list of points and find the points which minimize the OPT(n) formula, but I just don't follow it. It's making me feel stupid.</p> <p>I know this question is a pain in the ass and that it's not easy to answer but I'm just looking for some guidance towards understanding this algorithm. I apologize for the PDF but I don't have a neater way of getting the crucial information to the reader.</p> <p>Thank you for your time and reading this, I appreciate it.</p>
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    1. COThe linked document contains many algorithms. Which one are you looking at?
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    2. CO@pyfunc: Segmented least squares. Page 49/80. I believe you can click on the right hand sidebar under 'least segmented squares' and it will take you there as well.
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    3. COTrivia, this algorithm is due to Bellman and is some 50 years old, probably the first published example of DP.
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