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 e_{i, j} for the segment p_i … p_j
C is a constant that defines the range of allowable error

For j = 1 to n
    For i = 1 to j
        OPT(j) = min(e_{i, 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.