Lecture 13: Change Detection in Lines
On change detection in sequences of points. Segmented Least Squares with multi-way choices. Read section 6.3 in the book.
Algorithm:
For all pairs (i, j) | i <= j, compute the least squares error ei, j for the segment pi … pj
C is a constant that defines the range of allowable error
For j = 1 to n
For i = 1 to j
OPT(j) = min(ei, j + C + OPT(i-1));
End For
EndFor
Return OPT(n)
Reasoning:
We partition the set of points into the set of all possible line segments. Then, for each line segment we compute the error of a least-squares fit through that line segment. Then, we iterate through all the line segments, finding the last point which has “acceptable” error, otherwise starting a new subsequence. In this way, we choose an optimal number and location of least squares fits for our data.
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