Calculating identity vectors

After the alignment of C S B _Vs, identity vectors (I _V) are created for every C S B _V. All I _Vs have the same length and they represent the percentage of identity that a certain region of length W has in the alignment. We take a window of length W to calculate that percentage of identity.

First we create a binary vector (V _B) which represents matches in the alignment. V _B has the length of the alignment. Since V _B takes into account gaps, its length can be different from one C S B _V to another. By using a window of length W, we can compute the percentage of identity at any point in V _B. As long as we are going to compare I _V from different C S B _Vs, identity values from those points in the alignment that represent a gap in sequence X are not stored. This way, all identity vectors from different C S B _Vs will have the same length, R O I _length.

Low values in parameter W produce a noisy identity vector corresponding with high frequency changes of identity. On the contrary, high values in parameter W smooth the noise and produce a low frequency signal. The selection of a proper W value is not possible as it might change depending on the C S B _V involved. We could also be interested on changes that happen at different frequencies. Therefore, instead of choosing a fixed W value, which would mean changes at only one frequency, we build a vector containing all frequencies as follows:

where A _i is the weight of the identity vector at a certain frequency

And the Identity vector at a certain frequency is calculated as follows:

In this model, N defines the maximum window to compute the percentage of identity and also defines the start and end positions where the values of the vector can be used. From 0 to 2N+1 and from 2N+1−R O I _length to R O I _length the I _V is uncompleted. Therefore, N cannot be as long as we want. It should be at least lesser than OFFSET. In practice we have observed that a value of 50 is enough to get good results.

Finally, since identity vectors are going to be compared, they must to be normalized.