is cooler balance default using ICE normalization

[jiangshan529]

Hi, Is cooler balance default using ICE normalization? How can I view the ICE normalized matrix and used it for downstream analysis? Thanks!

[nvictus]

Yes, ICE (really, just iterative correction (IC) -- the E is a separate and unrelated step) is an implementation of an operation on matrices known as matrix balancing in the numerical linear algebra community and iterative proportional fitting in the statistics community. There's an insightful blog post by Lior Pachter on the subject.

The IC algorithm is essentially a variant of the Sinkhorn-Knopp algorithm tailored to a symmetric matrix. Other algorithms, like KR, solve the exact same numerical problem but have different theoretical convergence rates and stability tradeoffs.

Cooler balance's default normalization is matrix balancing, calculated using the IC method, applied genome-wide (rather than by chromosome in cis).

Depending how you query the matrix, the normalization can be applied automatically. If you query the raw counts, you can also apply the normalization manually by multiplying each pixel A_ij by the corresponding balancing weights w_i, w_j. The weights are stored in the bin table as a column called weight.

Hope that answers your question.