Normalization of Hi-C maps

To normalize the Hi-C maps, several methods are implemented.

• Iterative Correction (IC) [1] This method normalize the raw contact map by removing biases from experimental procedure. This is an method of matrix balancing, however, in the normalized, sum of rows and columns are not equal to one.
• Knight-Ruiz Matrix Balancing (KR) [2] The Knight-Ruiz (KR) matrix balancing is a fast algorithm to normalize a symmetric matrix. A doubly stochastic matrix is obatined after this normalization. In this matrix, sum of rows and columns are equal to one.
• Median Contact Frequency Scaling (MCFS) This method can be used to normalize contact map using Median contact values for particular distance between two locations/coordinates. At first, Median distance contact frequency for each distance is calculated. Subsequently, the observed contact frequency is divided by median contact frequency obtained for distance between the two locations.

To perform these normalizations, following tools are implemented:

• cmapNormalizer : A GUI application for normalization
• normKR : Normalization by Knight-Ruiz matrix balancing
• normIC : Normalization by Iterative Correction
• normMCFS : Scale maps using Median/Mean Contact Frequency

References

[1]	Imakaev et al. Iterative correction of Hi-C data reveals hallmarks of chromosome organization. Nature Methods 9, 999–1003 (2012).

[2]	Knight P and D. Ruiz. A fast algorithm for matrix balancing. IMA J Numer Anal (2013) 33 (3): 1029-1047.