Algorithm on how to calculate the sum of partial residuals

Question

[asifnax]

Hi,

Please see the equation below:

VJi  = max1<=s<=e<=J |sigma e  j=s(rij)| /sqrt(e-s +1)

It is from this paper:

http://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-10-156

Equation (3).

Its based on the sum of partial residuals but clarification would be welcomed

Thanks

[GenoMax]

This questions is not directly related to bioinformatics (unless you provide additional context in your post). It will most likely be closed unless you do so soon.

[GenoMax]

Equation in original question.

[russhh]

which part of the expression don't you follow - how to compute it, or what it represents?

[asifnax]

Hi,

What it represents i.e. how are residuals being summed together.

Thanks

[Emily]

A meaningful title would help too.

[asifnax]

Could the admin the change the title to "Algorithm on how to calculate the sum of partial residulas ?"

[asifnax]

Can anyone explain the 'max' bit ?

[russhh]

For a given value of i and J, you compute the fraction for each pair of values e,s such that 1 <= s <= e <= J. Having done this, you have K possible values, say (one for each pair e,s) and you set the value of v ^{(J)} _{i} to the largest of the K values

This is quite standard mathematical notation

[asifnax]

So what are 'e' and 's' exactly ?

Also do you have links that explain this notion?

[russhh]

They are numbers between 1 and J, where J is the number of probes on the array. The paper is quite explicit: e takes every value from 1 to J, and for a given e, s takes every value from 1 to e.

You really have to get to grips with scientific / mathematical notation. Go to the library and get a maths book out

[asifnax]

Thanks, I understand - you add two residuals every time from consecutive probes 1 ,1+2 ,2, 2+3 , 3, 3+4 ... and from them the highest is chosen as the MUF score.

[russhh]

Not quite. Suppose as an example, J=10, s = 2, e = 9. Then 1 <= s <= e <= J. and you have to add up r[i, j] for j=s..e. That is you do r[i, 2] + r[i, 3] + ... + r[i, 9], take the abs of that and divide it by sqrt(8). [this process is repeated for e = 1..10, s = e..10] Have you come across sigma notation before?

[asifnax]

Yes, sigma is the summation, here it is used to sum residuals from e to s, i think.

The different s and e permutations is the most hardest part of the equation but I think you have cleared it up.

I think its called a selection algorithm.