Running Median? Piecewise?

[Will Foran]

I have 14 unique values in a 66x1 matrix ranging from 0.000something to 0.00something of PRD thresholds. Calculating this accomplishes what the paper does  iteratively (removing genes until all the set size no longer decreases)? 

Does this also take care of the "running median" (paper pg10 and lecture 14-s31)?

In 1.4, should we only be looking at a least squares fit?

Also, the paper appears to have a single continuous line. Is this ultimately our goal? Our results should be visibly piecewise?

[Aparna Kumar]

1.4 you need to determine the line segments.  You should have a new segment for every set of invariant genes, which is determined from every threshold. 

To plot a line segment you need to calculate a slope (m) and an intercept (b).  Question 1.4 is helping you understand how to find these two parameters.  The parameters are found by considering the invariant genes in a segment and by making sure that the line is continuous (see Murats post of our discussion from earlier today).  This can be done by a least squares fit, where you are minimizing over a parameter (m).  Since we are working with linear pieces would you expect to find a closed form solution for this?  (another hint, answer = yes)  Write this closed form down for 1.4 and implement it in 1.5.  

The results are (and look) piecewise.