# 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 obtained after this normalization. In this matrix, sum of rows and columns are equal to one.**Vanilla-Coverage**(VC) [3] This method was first used for inter-chromosomal map. Later it was used for intra-chromosomal map by Rao et al., 2014. This is a simple method where at first each element is divided by sum of respective row and subsequently divided by sum of respective column.**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:**

## 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. |

[3] | Lieberman-Aiden et al. Comprehensive mapping of long-range interactions reveals
folding principles of the human genome.
Science (2009) 326 : 289-293. |